Maths-
General
Easy

Question

If z1, z2, z3 are complex numbers such that∣z1∣=∣ z2 ∣=∣ z3 ∣=open vertical bar fraction numerator 1 over denominator z subscript 1 end subscript end fraction plus fraction numerator 1 over denominator z subscript 2 end subscript end fraction plus fraction numerator 1 over denominator z subscript 3 end subscript end fraction close vertical bar equals 1, thus, ∣ z1 + z2 + z3 ∣ is

  1. equal to 1    
  2. less than 1    
  3. greater than 3    
  4. equal to 3    

The correct answer is: equal to 1


    ∣ z subscript 1 end subscript ∣ equals ∣ z subscript 2 end subscript ∣ equals ∣ z subscript 3 end subscript ∣ equals 1
    Error converting from MathML to accessible text.
    Hence Error converting from MathML to accessible text.

    Related Questions to study

    General
    Maths-

    If the roots of the equation z2 + az + b = 0 are purely imaginary, then

    If the roots of the equation z2 + az + b = 0 are purely imaginary, then

    Maths-General
    General
    Maths-

    The cube roots of unity

    The cube roots of unity

    Maths-General
    General
    Maths-

    If z satisfies ∣ z − 1∣ < ∣ z + 3 ∣, then omega = 2z + 3 − i satisfies :

    If z satisfies ∣ z − 1∣ < ∣ z + 3 ∣, then omega = 2z + 3 − i satisfies :

    Maths-General
    parallel
    General
    Maths-

    A(z1), B(z2) and C(z3) be the vertices of an equilateral triangle in the argand plane such that ∣z1∣ = ∣z2∣ = ∣z3∣. Then which of the following is false ?

    A(z1), B(z2) and C(z3) be the vertices of an equilateral triangle in the argand plane such that ∣z1∣ = ∣z2∣ = ∣z3∣. Then which of the following is false ?

    Maths-General
    General
    Maths-

    If the system of equations x-ky-z=0,kx-y-z=0,x+y-z=0 has a non-zero solution then the possible values of k are

    For such questions, we should remember the requirement for non zero solution. We have to be careful when finding the determinant.

    If the system of equations x-ky-z=0,kx-y-z=0,x+y-z=0 has a non-zero solution then the possible values of k are

    Maths-General

    For such questions, we should remember the requirement for non zero solution. We have to be careful when finding the determinant.

    General
    Maths-

    If A equals open square brackets table row cell fraction numerator 1 over denominator 2 end fraction open parentheses e to the power of i x end exponent plus e to the power of negative i x end exponent close parentheses end cell cell fraction numerator 1 over denominator 2 end fraction open parentheses e to the power of i x end exponent minus e to the power of negative i x end exponent close parentheses end cell row cell fraction numerator 1 over denominator 2 end fraction open parentheses e to the power of i x end exponent minus e to the power of negative i x end exponent close parentheses end cell cell fraction numerator 1 over denominator 2 end fraction open parentheses e to the power of i x end exponent plus e to the power of negative i x end exponent close parentheses end cell end table close square brackets then A to the power of negative 1 end exponent exists

    Whenever we have to find the inverse of the matrix, we should check the determinant of the matrix. The determinant must be non zero for a inverse to exist.

    If A equals open square brackets table row cell fraction numerator 1 over denominator 2 end fraction open parentheses e to the power of i x end exponent plus e to the power of negative i x end exponent close parentheses end cell cell fraction numerator 1 over denominator 2 end fraction open parentheses e to the power of i x end exponent minus e to the power of negative i x end exponent close parentheses end cell row cell fraction numerator 1 over denominator 2 end fraction open parentheses e to the power of i x end exponent minus e to the power of negative i x end exponent close parentheses end cell cell fraction numerator 1 over denominator 2 end fraction open parentheses e to the power of i x end exponent plus e to the power of negative i x end exponent close parentheses end cell end table close square brackets then A to the power of negative 1 end exponent exists

    Maths-General

    Whenever we have to find the inverse of the matrix, we should check the determinant of the matrix. The determinant must be non zero for a inverse to exist.

    parallel
    General
    Maths-

    If l subscript 1 end subscript superscript 2 end superscript plus m subscript 1 end subscript superscript 2 end superscript plus n subscript 1 end subscript superscript 2 end superscript equals 1 comma etc., and l subscript 1 end subscript l subscript 2 end subscript plus m subscript 1 end subscript m subscript 2 end subscript plus n subscript 1 end subscript n subscript 2 end subscript equals 0 comma etc. and capital delta equals open vertical bar table row cell l subscript 1 end subscript end cell cell m subscript 1 end subscript end cell cell n subscript 1 end subscript end cell row cell l subscript 2 end subscript end cell cell m subscript 2 end subscript end cell cell n subscript 2 end subscript end cell row cell l subscript 3 end subscript end cell cell m subscript 3 end subscript end cell cell n subscript 3 end subscript end cell end table close vertical bar then

    If l subscript 1 end subscript superscript 2 end superscript plus m subscript 1 end subscript superscript 2 end superscript plus n subscript 1 end subscript superscript 2 end superscript equals 1 comma etc., and l subscript 1 end subscript l subscript 2 end subscript plus m subscript 1 end subscript m subscript 2 end subscript plus n subscript 1 end subscript n subscript 2 end subscript equals 0 comma etc. and capital delta equals open vertical bar table row cell l subscript 1 end subscript end cell cell m subscript 1 end subscript end cell cell n subscript 1 end subscript end cell row cell l subscript 2 end subscript end cell cell m subscript 2 end subscript end cell cell n subscript 2 end subscript end cell row cell l subscript 3 end subscript end cell cell m subscript 3 end subscript end cell cell n subscript 3 end subscript end cell end table close vertical bar then

    Maths-General
    General
    Maths-

    If A equals open square brackets table row alpha 0 row 1 1 end table close square brackets and B equals open square brackets table row 1 0 row 3 1 end table close square brackets comma then value of alpha for which A to the power of 2 end exponent equals B is

    For such questions, we should know how to multiply to matrices. When there is equal sign between two matrices, the elements of both the matrix should be equal.

    If A equals open square brackets table row alpha 0 row 1 1 end table close square brackets and B equals open square brackets table row 1 0 row 3 1 end table close square brackets comma then value of alpha for which A to the power of 2 end exponent equals B is

    Maths-General

    For such questions, we should know how to multiply to matrices. When there is equal sign between two matrices, the elements of both the matrix should be equal.

    General
    Maths-

    For the primitive integral equation y d x plus y to the power of 2 end exponent d y equals x d y comma x element of R comma y greater than 0 comma y equals y open parentheses x close parentheses comma y open parentheses 1 close parentheses equals 1 comma then y open parentheses negative 3 close parentheses is

    For such questions, we should know different method of differentiation and integration.

    For the primitive integral equation y d x plus y to the power of 2 end exponent d y equals x d y comma x element of R comma y greater than 0 comma y equals y open parentheses x close parentheses comma y open parentheses 1 close parentheses equals 1 comma then y open parentheses negative 3 close parentheses is

    Maths-General

    For such questions, we should know different method of differentiation and integration.

    parallel
    General
    Maths-

    The differential equation of all circles which pass through the origin and whose centre lies on y-axis is

    For such questions, we should know the equation of cricle with its centre at a point other than origin.

    The differential equation of all circles which pass through the origin and whose centre lies on y-axis is

    Maths-General

    For such questions, we should know the equation of cricle with its centre at a point other than origin.

    General
    Maths-

    The differential equation of all parabolas whose axis are parallel to y-axis is

    For such questions, we should know how to write the equation of a parabola. The axis of parabola can be parallel to x or y axis. So, we have to write the equation accordingly.

    The differential equation of all parabolas whose axis are parallel to y-axis is

    Maths-General

    For such questions, we should know how to write the equation of a parabola. The axis of parabola can be parallel to x or y axis. So, we have to write the equation accordingly.

    General
    Maths-

    Solution of the differential equation open parentheses fraction numerator d y over denominator d x end fraction close parentheses to the power of 2 end exponent minus fraction numerator d y over denominator d x end fraction open parentheses e to the power of x end exponent plus e to the power of negative x end exponent close parentheses plus 1 equals 0 is given by

    When we get multipliction of two brackets equal to zero, any of the bracket can be zero or both of the brackets can be zero. It is decided based on the conditions in the equation.

    Solution of the differential equation open parentheses fraction numerator d y over denominator d x end fraction close parentheses to the power of 2 end exponent minus fraction numerator d y over denominator d x end fraction open parentheses e to the power of x end exponent plus e to the power of negative x end exponent close parentheses plus 1 equals 0 is given by

    Maths-General

    When we get multipliction of two brackets equal to zero, any of the bracket can be zero or both of the brackets can be zero. It is decided based on the conditions in the equation.

    parallel
    General
    Maths-

    The differential equation of all ellipse centred at the origin and major and minor axes along coordinate axes is

    The differential equation of all ellipse centred at the origin and major and minor axes along coordinate axes is

    Maths-General
    General
    Maths-

    Area of the region bounded by y equals tan invisible function application x comma tangent drawn to the curve at x equals fraction numerator pi over denominator 4 end fraction and the x minusaxis is

    Area of the region bounded by y equals tan invisible function application x comma tangent drawn to the curve at x equals fraction numerator pi over denominator 4 end fraction and the x minusaxis is

    Maths-General
    General
    Maths-

    Maximum value of x left parenthesis 1 minus x right parenthesis to the power of 2 end exponent, when 0 less or equal than x less or equal than 2, is

    Maximum value of x left parenthesis 1 minus x right parenthesis to the power of 2 end exponent, when 0 less or equal than x less or equal than 2, is

    Maths-General
    parallel

    card img

    With Turito Academy.

    card img

    With Turito Foundation.

    card img

    Get an Expert Advice From Turito.

    Turito Academy

    card img

    With Turito Academy.

    Test Prep

    card img

    With Turito Foundation.