The complex number z = i - 1 cos π 3 + i sin π 3 is equal to:

Question

The complex number z = i - 1 cos &#960; 3 + i sin &#960; 3 is equal to:

Aicharya · Accepted Answer

Given, z = i - 1 cos &#960; 3 + i sin &#960; 3 &#8658; z = 2 - 1 2 + i 2 cos &#960; 3 + i sin &#960; 3 Now argument of complex number - 1 2 + i 2 is 3 &#960; 4 So, by euler's formula e i &#952; = cos &#952; + i sin &#952; we get, &#8658; z = 2 e i 3 &#960; / 4 e i &#960; / 3 &#8658; z = 2 e i 5 &#960; / 12 &#8658; z = 2 cos 5 &#960; 12 + i sin 5 &#960; 12

The complex number z = i - 1 cos &#960; 3 + i sin &#960; 3 is equal to:

Solution

The complex number z = i - 1 cos π 3 + i sin π 3 is equal to: