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Given that z = a + bj, find Re(z/z) and Im(z/z).

By definition z* = a - bj.

We can write z/z* = ((a+bj)/(a-bj))*(a+bj)/(a+bj).

We calculate this to be z/z* = (a^2-b^2)/(a^2+b^2) + j(2ab)/(a^2+b^2).

Therefore, Re(z/z*) = (a^2-b^2)/(a^2+b^2).

Im(z/z*) = (2ab)/(a^2+b^2).

PJ

Answered by Penelope J. • Further Mathematics tutor

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