# Thread: Product of complex numbers.

1. ## Product of complex numbers.

I am having trouble simplifying this: (-5+3i)^2

and I don't understand how to divide:
(3-4i)/(5-2i)

Any help would be great

2. Originally Posted by Joaco
I am having trouble simplifying this: (-5+3i)^2

and I don't understand how to divide:
(3-4i)/(5-2i)

Any help would be great

it's just as you wrote :

$(-5+3i)(-5+3i ) = 25-15i-15i-9 = 16-30i$

P.S. because $i^2 = -1$

and for that problem with dividing that two complex numbers ...

$\displaystyle \frac {3-4i}{5-2i}$

multiply now with ...

$\displaystyle \frac {3-4i}{5-2i} \cdot \frac {5+2i}{5+2i} = \frac {(3-4i)(5+2i)}{(5-2i)(5+2i)}$

can you continue ?

3. Originally Posted by Joaco
I am having trouble simplifying this: (-5+3i)^2

and I don't understand how to divide:
(3-4i)/(5-2i)

Any help would be great
For division, standard procedure is to multiply numerator and denominator by the conjugate of the denominator (thus making the denominator a real number).

4. Learn this useful formula: $\displaystyle \frac{z}{w}=\frac{z\cdot \overline{w}}{|w|^2}$.

So $\displaystyle \frac{3-4i}{5-2i}=\frac{(3-4i)(5+2i)}{29}$

5. Originally Posted by yeKciM

and for that problem with dividing that two complex numbers ...

$\displaystyle \frac {3-4i}{5-2i}$

multiply now with ...

$\displaystyle \frac {3-4i}{5-2i} \cdot \frac {5+2i}{5+2i} = \frac {(3-4i)(5+2i)}{(5-2i)(5+2i)}$

can you continue ?

So it would be (23 - 14i)/ 29

Originally Posted by Plato
Learn this useful formula: $\displaystyle \frac{z}{w}=\frac{z\cdot \overline{w}}{|w|^2}$.

So $\displaystyle \frac{3-4i}{5-2i}=\frac{(3-4i)(5+2i)}{29}$
It makes a lot of sense

Thank you everyone