# Thread: Complex Numbers Problem

1. ## Complex Numbers Problem

The question is (8 + 20i) / (2i)
So I think that I have to multiply that by (-2i)/(-2i), but I'm not sure?
Also, It wants me to write the result in standard form?

Any help is appreciated.

2. Originally Posted by tsmith
The question is (8 + 20i) / (2i)
So I think that I have to multiply that by (-2i)/(-2i), but I'm not sure?
Also, It wants me to write the result in standard form?

Any help is appreciated.
correct ... multiply numerator and denominator by the conjugate of $2i$ , which is $-2i$

remember that $i^2 = -1$

standard form is $a + bi$

do it.

3. (8+20i)/(2i) multiple (-2i)/(-2i) = (-16i - 40i^2)/(-4i^2) = (-16i+40)/(4) =
-4i + 10

Is this the correct answer?

4. Originally Posted by tsmith
(8+20i)/(2i) multiple (-2i)/(-2i) = (-16i - 40i^2)/(-4i^2) = (-16i+40)/(4) =
-4i + 10

Is this the correct answer?
yes

5. Here is one of the most important and over-looked ideas.
$\frac{z}{w} = \frac{{z\overline w }}{{\left| w \right|^2 }}$.

Thus: $\frac{{8 + 2i}}{{2i}} = \frac{{\left( {8 + 2i} \right)\left( { - 2i} \right)}}{4}$