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
6875 Views
See similar Further Mathematics A Level tutorsRelated Further Mathematics A Level answers
All answers ▸It is given that f(x) = 2sinhx+3coshx. Show that the curve y = f(x) has a stationary point at x =-½ ln(5) and find the value of y at this point. Solve the equation f(x) = 5, giving your answers exactly
Prove by induction that 11^n - 6 is divisible by 5 for all positive integer n.
I'm struggling with an FP2 First-Order Differential Equations Question (Edexcel June 2009 Q3) and the topic in general!
Further Maths: How do you find the inverse of a 2 x 2 matrix?