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

5186 Views

See similar Further Mathematics A Level tutors

Related Further Mathematics A Level answers

All answers ▸

Solve the equation 3sinh(2x) = 13 - 3e^(2x), answering in the form 0.5ln(k). where k is an integer


Find values of x which satisfy the inequality: x^2-4x-2<10


Find the eigenvalues and eigenvectors of A = ([2, 0 , 0], [0, 1, 1], [0, 3, 3])


Let A, B and C be nxn matrices such that A=BC-CB. Show that the trace of A (denoted Tr(A)) is 0, where the trace of an nxn matrix is defined as the sum of the entries along the leading diagonal.


We're here to help

contact us iconContact usWhatsapp logoMessage us on Whatsapptelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences