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In the complex number system, what is the value of $16 i to the power of 4 minus 8 i squared plus 4 ?$ ? (Note: $i equals square root of negative 1 end root right parenthesis$

hint Hint:

Hint:
$i equals square root of negative 1 end root$ is called ‘iota’ or the imaginary number. It is the solution of the quadratic equation $x squared plus 1 equals 0$ . It is used to denote a complex number. A complex number is written in the form of $a plus i b$ , where $i equals square root of negative 1 end root$ .
Here, first we need to find the value of $i to the power of 4$ and $i squared$ then put it in the given expression to find its value.

The correct answer is: 28

First, we find the value of $i squared$ .
We are given,
$i equals square root of negative 1 end root$
Squaring both sides, we get
$i squared equals left parenthesis square root of negative 1 end root right parenthesis squared$
$i squared equals negative 1$
So, we get $i squared equals negative 1$ .
Again, squaring both sides of $i squared equals negative 1$ , we get
$open parentheses i squared close parentheses squared equals left parenthesis negative 1 right parenthesis squared$
$i to the power of 4 equals 1$
Thus, we get the values $i squared equals negative 1$ and $i to the power of 4 equals 1$
Putting these values in the expression $16 i to the power of 4 minus 8 i squared plus 4$ , we get
$16 left parenthesis 1 right parenthesis minus 8 left parenthesis negative 1 right parenthesis plus 4$
$equals 16 plus 8 plus 4$
$equals 28$
Hence, we get the value of the expression
$16 i to the power of 4 minus 8 i squared plus 4 equals 28$
The correct answer is 28.

.

.

Note:
It is advised to memorize the values of powers of i , that is ,
$i squared equals negative 1 comma i cubed equals negative i comma i to the power of 4 equals 1 comma i to the power of 5 equals i text , etc. end text$
We can observe that $i to the power of 4 n end exponent equals 1$ for all natural number . Also, even powers of is always a real number n, either 1 or - 1

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In the complex number system, what is the value of ? (Note:

Hint: is called ‘iota’ or the imaginary number. It is the solution of the quadratic equation . It is used to denote a complex number. A complex number is written in the form of , where .Here, first we need to find the value of and then put it in the given expression to find its value.

The correct answer is: 28

First, we find the value of .We are given,Squaring both sides, we getSo, we get .Again, squaring both sides of , we getThus, we get the values andPutting these values in the expression , we getHence, we get the value of the expressionThe correct answer is 28...

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In the complex number system, what is the value of $16 i to the power of 4 minus 8 i squared plus 4 ?$ ? (Note: $i equals square root of negative 1 end root right parenthesis$

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(222, 525). A reflection of 𝐴𝐵 results in the image 𝑋𝑌, with coordinates X (-100, -111) and Y (-222, 525). Tell which axis 𝐴𝐵 was reflected in and write the coordinate rule for the reflection.

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(222, 525). A reflection of 𝐴𝐵 results in the image 𝑋𝑌, with coordinates X (-100, -111) and Y (-222, 525). Tell which axis 𝐴𝐵 was reflected in and write the coordinate rule for the reflection.

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