# Thread: How do you find the conjugate of -2/i^3?

1. ## How do you find the conjugate of -2/i^3?

What is the conjugate of $\frac{\ -2}{i^3}$?

2. ## Re: How do you find the conjugate of -2/i^3?

$\frac{-2}{i^3}=\frac{-2i}{i^4}=-2i$.

3. ## Re: How do you find the conjugate of -2/i^3?

To find the conjugate of any complex number, replace i with -i. You could "rationalize the denominator" first, as "a tutor" did:
$\frac{-2}{i^3}= -2i$ and then its conjugate is $-2(-i)= 2i$. Or you can immediately write that the conjugate is $\frac{-2}{(-i)^3}= \frac{2}{i^3}$. If you were then to multiply both numerator and denominator by i you would again get $\frac{2i}{i^4}= \frac{2i}{(i^2)^2}= \frac{2i}{(-1)^2}= 2i$.

4. ## Re: How do you find the conjugate of -2/i^3?

aw...i was gonna say find its minimal real polynomial, and grab the other root :P

5. ## Re: How do you find the conjugate of -2/i^3?

What's the reason you multiplied the numerator and denominator by i?

6. ## Re: How do you find the conjugate of -2/i^3?

Originally Posted by viccal
What's the reason you multiplied the numerator and denominator by i?
tutor used the fact that $i^4 = 1$ in order to get $\frac{-2}{i^3}$ in the form $a \pm bi$ in an efficient manner.

he ended up with $-2i = 0 - 2i$ ... note that the conjugate is $0 + 2i = 2i$