Question

9+3i divided by 4+8i

Answer 1

Answer:

$\frac{3}{4}-\frac{3}{4}i$

Step-by-step explanation:

$\frac{9+3i}{4+8i}$

I assume you want to rationalize the denominator (make it real). To do this, we will multiply top and bottom by bottom's cojugate.

$\frac{9+3i}{4+8i} \cdot \frac{4-8i}{4-8i}$

Use foil on top.

On bottom, since you are multiplying conjugates all you have to do is first times first and last times last.

$\frac{9(4)+9(-8i)+3i(4)+3i(-8i)}{4(4)+(8i)(-8i)}$

$\frac{36-72i+12i-24i^2}{16-64i^2}$

Recall $i^2=-1$.

$\frac{36-60i-24(-1)}{16+64}$

$\frac{36+24-60i}{16+64}$

$\frac{60-60i}{80}$

Both the numerator and denominator share a common factor of 20:

$\frac{3-3i}{4}$

You could also seperate the fraction like so:

$\frac{3}{4}-\frac{3}{4}i$