Question

Number of solutions of the equation `z^3+[3(barz)^2]/|z|=0` where z is a complex number is
A. 2
B. 3
C. 6
D. 5

Answer 1

Correct Answer - D
Given, `z^(3)+(3(barz)^(2))/(|z|)=0`
Let `z=re^(itheta)`
`rArr r^(3)e^(i3theta)+3re^(-2theta)=0`
Since r cannot be zero, so
`re^(i5theta)=-3`
Which will hold for r = 3 and five values of `theta`. Thus, there are five solution.