Complex number question

[385sk117]

Homework Statement

If z = cis @ where @ is acute, determine the modulus and argument of z-1

Homework Equations

The Attempt at a Solution

As the moudlus of z is 1 z lies on the unit circle. And I can not think of anything more. I drew a graph to see how z-1 seems like in graph and stucked.
Help me please!

 

[dx]

The modulus of x + iy is √(x² + y²) and the argument is tan^-1(y/x). Draw the vector in the complex plane to see why.

 

[385sk117]

That I know; but this thing is little different from the normal quetions where the number is multiplied to z such as -z, 2z etc which i can use that formula but here i think i should know some angles and shape of graph
I saw the answer and it was
moduls = 2 sin (@/2) argument = (@/2) + (pi/2)

 

[dx]

It's possible to do using just the formulas I wrote, but it's easier to do pictorially. Look at the attachment:

http://img99.imageshack.us/img99/86/picqrv.jpg [Broken]

 

[385sk117]

Wow i also drew some similar graph but couldn't understand what to do with that but by drawing the line at the middle everything become clear.
Thankyou so much!

 

[dx]

No problem.