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

5382 Views

See similar Further Mathematics A Level tutors

Related Further Mathematics A Level answers

All answers ▸

What is the meaning of having a 3 by 3 matrix with determinent 0. Both geometrically and algebriaclly.


Using a Suitable substitution or otherwise, find the differential of y= arctan(sinxcosx), in terms of y and x.


The finite region bounded by the x-axis, the curve with equation y = 2e^2x , the y-axis and the line x = 1 is rotated through one complete revolution about the x-axis to form a uniform solid. Show that the volume of the solid is 2π(e^2 – 1)


Find y in terms of x for the equation 2x(dy/dx) + 4y = 8x^2


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences