# Question involving complex numbers

• Nov 16th 2012, 11:11 PM
Tutu
Question involving complex numbers
Hi I really do not know how to do this.

Write sin2a-cos2ai in modulus argument form
I was thinking of changing sin2a to cos(pi/2 - 2a)..

Will really appreciate the help! Thanks,
J.
• Nov 16th 2012, 11:22 PM
chiro
Re: Question involving complex numbers
Hey Tutu.

What is modulus argument form? Is that in terms of re^(i*theta) where r = 1?
• Nov 16th 2012, 11:26 PM
Prove It
Re: Question involving complex numbers
Quote:

Originally Posted by Tutu
Hi I really do not know how to do this.

Write sin2a-cos2ai in modulus argument form
I was thinking of changing sin2a to cos(pi/2 - 2a)..

Will really appreciate the help! Thanks,
J.

Notice this is in the Cartesian Form \displaystyle \begin{align*} x + y\,i \end{align*} with \displaystyle \begin{align*} x = \sin{(2a)} \end{align*} and \displaystyle \begin{align*} y = \cos{(2a)} \end{align*}. You need to write it in the modulus-argument form \displaystyle \begin{align*} r\, e^{i\,\theta} \end{align*} with \displaystyle \begin{align*} r = \sqrt{x^2 + y^2} \end{align*} and \displaystyle \begin{align*} \theta = \arctan{\left( \frac{y}{x} \right)} \end{align*}.
• Nov 16th 2012, 11:42 PM
Tutu
Re: Question involving complex numbers
From what I've learnt, modulus-argument form is the polar form where it is rcis(thetha) where r is positive.
re^i(thetha) is exponential form for me.

The answer of this question is in cis form, not exponential form.
• Nov 17th 2012, 12:14 AM
Prove It
Re: Question involving complex numbers
Quote:

Originally Posted by Tutu
From what I've learnt, modulus-argument form is the polar form where it is rcis(thetha) where r is positive.
re^i(thetha) is exponential form for me.

The answer of this question is in cis form, not exponential form.

The calculation of \displaystyle \begin{align*} r \end{align*} and \displaystyle \begin{align*} \theta \end{align*} is identical.
• Nov 17th 2012, 12:56 AM
Tutu
Re: Question involving complex numbers
Sorry, I do not understand..
Can you show me how you would do it?
• Nov 17th 2012, 01:14 AM
Prove It
Re: Question involving complex numbers
You already have x and y. Evaluate \displaystyle \begin{align*} r = \sqrt{x^2 + y^2} \end{align*} and \displaystyle \begin{align*} \theta = \arctan{\left( \frac{y}{x} \right)} \end{align*}.