Question

复数|z1+z2|^2的平方等于什么?

Answer 1

设z1=a+bi

z2=c+di

|z1+z2|=|a+bi+c+di|=|(a+c)+(b+d)i|=[(a+c)^2+(b+d)^2]^(1/2)

所以|z1+z2|^2|=|a+bi+c+di||^2

=[(a+c)^2+(b+d)^2]

=[a^2+2ac+c^2+b^2+2bd+d^2]

=[a^2+b^2+c^2+d^2+2(ac+bd)]