Mathegoras

Complex numbers › Roots of unity and complex roots › Counting complex solutions

Pairs of unit complex numbers

High school · ●●○○○ 20 pts

Find the number of pairs (z1,z2)(z_1,z_2) of complex numbers such that z1z2z_1 z_2 is pure imaginary, z1z2\frac{z_1}{z_2} is real, and ∣z1∣=∣z2∣=1|z_1| = |z_2| = 1.

Sign in to save your progress.

modulus of complex numberscounting