# Math Help - can anyone help me complex number question?

1. ## can anyone help me complex number question?

Let x = 2e-(p/4)i, y = 3e(p/6)i. Let a + bi = x2 / y3. Find a and b.
I do not have any idea for this question.

2. Originally Posted by eunse16
Let x = 2e-(p/4)i, y = 3e(p/6)i. Let a + bi = x2 / y3. Find a and b.
I do not have any idea for this question.
I have no idea what the given numbers are. Are they
$x = 2e^{-\frac{p}{4}i}$
$y = 3e^{\frac{p}{6}i}$?
And is p pi?

01

3. ## Yes

Sorry.
you are right. I made a mistake.
P is pi.

4. If the numbers are indeed $x=2e^{-\frac{\pi i}{4}}~\&~x=2e^{\frac{\pi i}{6}}$ then
$x^2=4e^{-\frac{\pi i}{2}}=-4i$
$y^3=27e^{\frac{\pi i}{2}}=27i$
$\frac{x^2}{y^3}=\frac{-4}{27}$

5. Using, of course, the laws of exponents: $\left(e^{ax}\right)^n= e^{nax}$ and $\frac{e^{ax}}{e^{bx}}= e^{(a-b)x}$.