A Cubic Modulus Minimum

★ 8/10complex numbers Estimation Symmetry

Problem

Complex numbers $z_1, z_2$ satisfy

|z_1 + z_2| = 20, \qquad |z_1^2 + z_2^2| = 16.

Find the minimum value of $|z_1^3 + z_2^3|$ .

Answer

Solution

Difficulty	8/10
Topics	complex numbers, Estimation, Symmetry

Whiteboard

Your sketch is saved only in this browser. To share it, export your drawing as an image (whiteboard menu → Export as → PNG), then upload that image in the comments below.

Discussion

Ask questions, share alternate solutions, and use LaTeX freely.

0 comments

No comments yet.