Number of solutions of the equation z3+3(z¯)2|z|=0 where z is a complex number is

Given,z3+3(z¯)2|z|=0Let z=reiθ⇒r3ei3θ+3re−i2θ=0Since r cannot be zero, sor2ei5θ=−3which will hold for r2=3 and five distinct values of θ Thus, there are five solutions