Question

In: Math

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

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

Solutions

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.


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