Complex numbers are complex
Algebra
Level
3
Let z be a complex number satisfying z+|z|=2+8i. Find the magnitude of z squared. Source : AOPS
The answer is 289.
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1 solution
let z=a+ib now as per given we have
a+ib+(a^2+b^2)^(1/2)=2+8i comparing real and img. part we have
b=8 and a++(a^2+b^2)^(1/2)=2 -------(1) on solving(1)
we have a=-15 hence z=-15+8i and on squaring both sides we have z^2=161-240i
so |z^2|=(161^2+(-240)^2)^(1/2)=289