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

[Joza]

IS there a formula for:

z=(Cosx +iSinx)^4 (Cosy + iSiny)^2 ??

 

[daveb]

You mean a way to simplify it? Just change each expression in ( ) to its corresponding exponential form.

 

[Werg22]

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.

 

[Joza]

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?

 

[Werg22]

If so, have you tried, as daveb suggested$$z=(\cos x +i\sin x)^{4} * (\cos y + i\sin y)^{2}$$

$$z = e^{4xi} * e^{2yi}$$

$$z = e^{(4x + 2y)i}$$

$$z = \cos (4x + 2y) + i \sin (4x + 2y)$$

 

[Joza]

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!