# Thread: Complex number arguments

1. ## Complex number arguments

Hi I don't understand how the answer to this question came about.

Find the argument expressed in the range of (-pi , pi] of -3ie-(iπ/4)

Thank you! Why is it not -pi/4?

2. ## Re: Complex number arguments

Because $\displaystyle -3i=3e^{i\pi}e^{i\frac{\pi}{2}}$

3. ## Re: Complex number arguments

Originally Posted by princessp
Hi I don't understand how the answer to this question came about.

Find the argument expressed in the range of (-pi , pi] of -3ie-(iπ/4)

Thank you! Why is it not -pi/4?
I think that you are correct. See HERE.

4. ## Re: Complex number arguments

You've entered the wrong expression into Wolfram Alpha. Rubbish in -> rubbish out.

5. ## Re: Complex number arguments

Originally Posted by Archie
Because $\displaystyle -3i=3e^{i\pi}e^{i\frac{\pi}{2}}$
just to finish this (because it was confusing me)

$-3i = 3e^{i \pi}e^{i \pi/2} = 3e^{3\pi/2} \to 3 e^{-\pi/2}$

because $\dfrac {3\pi}{2} > \pi$

now

$3 e^{-\pi/2}e^{-\pi/4} = 3 e^{-3\pi/4}$

$Arg\left( 3 e^{-3\pi/4}\right) = -\dfrac {3\pi}{4}$

6. ## Re: Complex number arguments

Originally Posted by princessp
Hi I don't understand how the answer to this question came about.

Find the argument expressed in the range of (-pi , pi] of -3ie-(iπ/4)
Thank you! Why is it not -pi/4?
The correct answer is $\large\dfrac{-3\pi}{4}$ See HERE.

$\large\text{Arg}(-3\bf{i})=\dfrac{-\pi}{2}$ and $\large\text{Arg}\left(\exp(-\frac{\bf{i}\pi}{4}\right)=\dfrac{-\pi}{4}$ the sum of which is $\large\dfrac{-3\pi}{4}$