calculate the conjugate complex number of,z=(a+ib/a-ib)2+(a-ib/a+ib)2
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((a+ib)/(a-ib))2=(a+ib)4/(a2+b2)2;

((a-ib)/(a+ib))2=(a-ib)4/(a2+b2)2;

add these together:

((a+ib)4+(a-ib)4)/(a2+b2)2.

(a+ib)4=a4+4a3ib-6a2b2-4aib3+b4;

(a-ib)4=a4-4a3ib-6a2b2+4aib3+b4;

add these together:

2a4-12a2b2+2b4;

divide by (a2+b2)2:

2(a4-6a2b2+b4)/(a2+b2)2, which has only real components, making its conjugate the same as itself.

 

by Top Rated User (1.2m points)

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