Calculating Modulus and Argument of a Complex Number | Homework Question

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Homework Help Overview

The discussion revolves around determining the modulus and argument of a complex number expressed in polar form, specifically z = cis @, where @ is an acute angle. The original poster is exploring the properties of z-1 and how it relates to the unit circle.

Discussion Character

  • Exploratory, Conceptual clarification, Problem interpretation

Approaches and Questions Raised

  • The original poster attempts to visualize the problem by graphing z-1 but expresses difficulty in proceeding further. Some participants suggest using known formulas for modulus and argument, while others indicate that a pictorial approach may be more effective.

Discussion Status

Participants are actively engaging with the problem, sharing insights about graphical representations and the implications of the acute angle. There is an acknowledgment of the complexity of the problem compared to standard cases, and some guidance has been offered regarding the use of visual aids.

Contextual Notes

The original poster mentions feeling stuck and refers to the challenge posed by the specific form of the problem, which differs from typical scenarios involving straightforward multiplication of z. There is also a reference to an external image that may provide additional context.

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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!
 
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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
 
Last edited by a moderator:
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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