Question

Find a complex number a+ ????????????????, with aand ???????? positive real numbers, such that (a+ ????????????????)3 = i.

Answer 1

The complex number is 0+i/3.

Explanation:

Let the imaginary part be x.

The complex number will be a+xi

Given:

real part =a

(a+xi)*3=i...............(i)

To find:

imaginary part

Solution:

3a + 3xi=i.............(ii)

Comparing real and imaginary parts of eq(ii).

3a=0 and 3x=1

a=0

x=1/3.