# Thread: [SOLVED] Complex Numbers from Polar to Cartesian/Argand

1. ## [SOLVED] Complex Numbers from Polar to Cartesian/Argand

Hey,
So basically I have been given a complex number and I have tried converting it but I am worried that I am doing it wrong. $\displaystyle 3cis(pi/4)$

I was wondering if this complex number can come out exactly, and if there is a fast way of doing it/ checking it.

Thanks

2. $\displaystyle 3\cdot\text{cis}\frac{\pi}{4}$

$\displaystyle 3\cdot\text{cis}45$

$\displaystyle 3\cdot(\cos 45 + i \sin 45)$

You should know that $\displaystyle \cos 45 = \sin 45 = \frac{\sqrt{2}}{2}$.

3. Hello

Originally Posted by Evales
Hey,
So basically I have been given a complex number and I have tried converting it but I am worried that I am doing it wrong. $\displaystyle 3cis(pi/4)$

I was wondering if this complex number can come out exactly, and if there is a fast way of doing it/ checking it.

Thanks
$\displaystyle cis(x)=e^{ix}=\cos x+i \sin x$

Therefore, $\displaystyle 3 cis(\pi/4)=3e^{i \pi/4}=3(\cos \pi/4+i \sin \pi/4)$

Is it ok ?

To check it...hm, I don't see any other way >.< maybe a graphical one, but it's more complicated in my opinion.