Question

what is the value of root iota

Answer 1

Hey Friend!!! Here is one attachment☝☝that you can understand easily_______

The Value of root IOTA:--(SQUARE ROOT OF IOTA. SQUARE ROOT OF COMPLEX NUMBERS.
i, the square root of -1 the fundamental complex number.)

●Hope it will help you●

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Answer 2

The value of  $\sqrt{i}=\frac{1}{\sqrt{2}}+i \frac{1}{\sqrt{2}}$.

Imaginary number

An imaginary number is a real number multiplied by the imaginary unit i, which is defined by its property i² = −1

Explanation:

$\sqrt{i}$ can be written in form of real number + imaginary number

$\sqrt{i}=a+i b$

where,

$a$ is the real part and, $i b$ is the imaginary part.

Squaring both sides

$(\sqrt{i})^{2}=i=\left(a^{2}-b^{2}\right)+2 i a b$

Comparing real and imaginary terms on both side, we get

$2 a b=1$ and $a^{2}-b^{2}=0$

Therefore,

$\left(a^{2}+b^{2}\right)^{2}=\left(a^{2}-b^{2}\right)^{2}+4 a^{2} b^{2}$

$\left(a^{2}+b^{2}\right)^{2}=\lef1$

Solving further,

$a=b=\frac{1}{\sqrt{2}}$

Putting the values in the main equation, we get;

$\sqrt{i}=\frac{1}{\sqrt{2}}+i \frac{1}{\sqrt{2}}$

Thus, the value of root iota is found as $\sqrt{i}=\frac{1}{\sqrt{2}}+i \frac{1}{\sqrt{2}}$.

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