Question

if |Z^2-1| = |z| 2+1, prove that z lies on the imaginary axis

Answer 1

Answer:

Step-by-step explanation:

∣∣Z2−1∣∣=|Z|2+1

Square both sides

∣∣Z2−1∣∣2=(|Z|2+1)2

(Z2−1)(Z2−1)=(ZZ+1)2

Z2⋅Z2−Z2−Z2+1=(zZ)2+1+2ZZ

Z2+z2+2zZ=0

(Z+z)2=0

Z=x+iy

z=x−iy

x+iy=−(x−iy)

x+iy=−x+iy. x=−x,2x=0,x=0

Z is purely imaginally.