# Complex number question

## Homework Statement

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

## 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!

## Answers and Replies

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dx
Homework Helper
Gold Member
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.

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
Homework Helper
Gold Member
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]

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Wow i also drew some similar graph but couldnt understand what to do with that but by drawing the line at the middle everything become clear.
Thankyou so much!!!!!!!

dx
Homework Helper
Gold Member
No problem.