What Is the Modulus of z When z=(x-iy)/(x+iy)?

[alijan kk]

Homework Statement

if z=(x-iy)/(x+iy) then modulus of z is :

Homework Equations

The Attempt at a Solution

(x-iy)/(x+iy)= (x²-y²-2x(iy))/(x²+y²)

i can't get the real part and the imaginary part to take the modulus :

but the answer in any way could be = 1 ?

the answer in the book is 1 .

 

[DrClaude]

(x-iy)/(x+iy)= (x²-y²-2x(iy))/(x²+y²)

i can't get the real part and the imaginary part to take the modulus :

But you have it there. Simply split what you have on the right-hand side into real and imaginary parts.

 

[alijan kk]

But you have it there. Simply split what you have on the right-hand side into real and imaginary parts.

i got one the answer,
thank you so much :)

 

[ehild]

It is easier to use that $|z_1/z_2| = |z_1|/|z_2|$

 

[alijan kk]

It is easier to use that $|z_1/z_2| = |z_1|/|z_2|$

thanks a lot, it was actually a multiple choice question, and you gave me a quicker way