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
7062 Views
See similar Further Mathematics A Level tutorsRelated Further Mathematics A Level answers
All answers ▸Show that the matrix A is non-singular for all real values of a
Does the following matrix A = (2 2 // 3 9) (upper row then lower row) have an inverse? If the matrix A^2 is applied as a transformation to a triangle T, by what factor will the area of the triangle change under the transformation?
How does proof by mathematical induction work?
Explain the process of using de Moivre's Theorem to find a trigonometric identity. For example, express tan(3x) in terms of sin(x) and cos(x).