What is the Formula for Multiplying Complex Numbers in Polar Form?

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Discussion Overview

The discussion revolves around the formula for multiplying complex numbers expressed in polar form, specifically focusing on the expression z = (Cosx + iSinx)^4 (Cosy + iSiny)^2. Participants explore methods for simplifying this expression and the underlying principles of complex multiplication.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification

Main Points Raised

  • One participant asks if there is a formula for the given expression involving complex numbers in polar form.
  • Another participant suggests simplifying the expressions by converting them to their exponential form.
  • A different participant raises a concern about the interpretation of x and y, arguing that they should represent scalar values for the real and imaginary parts.
  • One participant clarifies that they are looking for a general method rather than specific values and inquires about the simplification process.
  • A later reply provides a step-by-step transformation of the expression into exponential form, ultimately expressing it in terms of cosine and sine.
  • Another participant acknowledges the final expression as something they have seen before, indicating familiarity with the result.

Areas of Agreement / Disagreement

Participants express differing views on the interpretation of the variables x and y, with some focusing on the method of simplification while others question the initial formulation. The discussion does not reach a consensus on the interpretation of the variables.

Contextual Notes

There are assumptions regarding the definitions of x and y, and the discussion does not resolve the implications of these assumptions on the expression. The steps for simplification are not fully detailed, leaving some mathematical processes unresolved.

Joza
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IS there a formula for:

z=(Cosx +iSinx)^4 (Cosy + iSiny)^2 ??
 
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You mean a way to simplify it? Just change each expression in ( ) to its corresponding exponential form.
 
This doesn't make any sense: one of x and y has to represent the real part scalar and the other the imaginary part scalar. The expression you have there implies that neither x nor y are scalars and hence aren't axial values.
 
Last edited:
Well I just put them in instead of the actual values...I'm just looking for the general way.

So do I simplify each and then multiply them or something?
 
If so, have you tried, as daveb suggested[tex]z=(\cos x +i\sin x)^{4} * (\cos y + i\sin y)^{2}[/tex]

[tex]z = e^{4xi} * e^{2yi}[/tex]

[tex]z = e^{(4x + 2y)i}[/tex]

[tex]z = \cos (4x + 2y) + i \sin (4x + 2y)[/tex]
 
Last edited:
I have only ever seen the last line there before, but that's actually what I thought it was. It's one of those rules.

Cheers guys!
 

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