Given-z-x-iy-z-C-z-0-1-A-B-and-C-are-the-images-of-z-iz-and-2-i-z-a-Calculate-the-lengths-AB-AC-and-BC-b-Deduce-that-the-triangle-ABC-is-isosceles-and-not-equilateral-2-Find-z-such-th

Question Number 97129 by Ar Brandon last updated on 06/Jun/20

Given z = x + iy z \in C z \neq 0

1 ∖ A, B, and C are the images of z, iz, and (2 - i) + z

a ∖ Calculate the lengths AB, AC, and BC .

b ∖ Deduce that the triangle ABC is isosceles and not

equilateral .

2 ∖ Find z, such that ∣ z ∣=∣ \frac{2 + i}{z} ∣=∣ z - 1 ∣

3 ∖ Given Z, Z \in C such that \frac{Z - 1}{Z + 1} = {(\frac{z - 1}{z + 1})}^{2}

a ∖ Express Z in terms of z

b ∖ What can we say of the images of Z, z, and \frac{1}{z} ?