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
7001 Views
See similar Further Mathematics A Level tutorsRelated Further Mathematics A Level answers
All answers ▸FP3- Find the eigenvalues and the eigenvector for the negative eigenvalue, from this 2x2 matrix of columns (2,1) and (3,0)
A curve has the equation (5-4x)/(1+x)
using an integrating factor, find the general solution of the differential equation dy/dx +y(tanx)=tan^3(x)sec(x)
Simplify (2x^3+8x^2+17x+18)/(x+2)