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 that ∣z∣=∣((2+i)/z)∣=∣z−1∣ 3\Given Z, Z∈C such that ((Z−1)/(Z+1))=(((z−1)/(z+1)))^2 a\Express Z in terms of z b\What can we say of the images of Z, z, and (1/z) ?


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Question Number 97129 by Ar Brandon last updated on 06/Jun/20
$Given z=x+iy z∈C z≠0 1\ A, B, and C are the images of z, iz, and (2−i)+z a\ Calculate the lengths AB, AC, and BC. b\ Deduce that the triangle ABC is isosceles and not equilateral. 2\Find z, such that ∣z∣=∣((2+i)/z)∣=∣z−1∣ 3\Given Z, Z∈C such that ((Z−1)/(Z+1))=(((z−1)/(z+1)))^2 a\Express Z in terms of z b\What can we say of the images of Z, z, and (1/z) ?$
$Given z = x + iy z \in C z \neq 0$ $1 ∖ A, B, and C are the images of z, iz, and (2 - i) + z$ $a ∖ Calculate the lengths AB, AC, and BC .$ $b ∖ Deduce that the triangle ABC is isosceles and not$ $equilateral .$ $2 ∖ Find z, such that ∣ z ∣=∣ \frac{2 + i}{z} ∣=∣ z - 1 ∣$ $3 ∖ Given Z, Z \in C such that \frac{Z - 1}{Z + 1} = {(\frac{z - 1}{z + 1})}^{2}$ $a ∖ Express Z in terms of z$ $b ∖ What can we say of the images of Z, z, and \frac{1}{z} ?$
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