Question

In: Math

Find the 4th roots of i. Sketch them in an Argand diagram.

Expert Solution

We need to find solution of the equation where is a complex number.

. Since is a non negative real number, therefore,

Using Euler's form:

(1) By Euler's formula:

(2)

By equation (1) and (2), , so,

The values of give 4 roots of unity.

The 4th roots of unity:

The points (1,0), (-1,0), (0,1), (0,-1) are 4th roots of unity in argand plane.

milcah answered 3 years ago

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