Calculating Modulus and Argument of a Complex Number | Homework Question

AI Thread Summary
The discussion focuses on determining the modulus and argument of the complex number z-1, where z is expressed as cis @. It is established that the modulus of z is 1, indicating it lies on the unit circle. The participant struggles with applying standard formulas for modulus and argument due to the unique nature of the problem, which involves visualizing the complex plane. The solution reveals that the modulus is 2 sin(@/2) and the argument is (@/2) + (π/2), suggesting that a graphical approach can clarify the problem. Overall, visualizing the complex number aids in understanding the calculations involved.
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Homework Statement



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


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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!
 
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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)
 
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
 
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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!
 
No problem.
 

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