Mathegoras

Complex numbers › The complex plane › Extremes of the modulus

Smallest modulus in a complex system

High school · ●●●○○ 50 pts

The complex numbers zz and ww satisfy the system z+20iw=5+i,w+12iz=−4+10i.\begin{align*} z + \frac{20i}{w} &= 5+i, \\ w+\frac{12i}{z} &= -4+10i. \end{align*} Find the smallest possible value of ∣zw∣2|zw|^2.

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systems of equationsquadratic equationsmodulus of complex numbers