Jazmin Perry

2022-02-01

How do you simplify $\frac{5-i}{3+3i}?$

ocretz56

Beginner2022-02-02Added 16 answers

Step 1

You must use something that resembles rationalization with roots at the denominator: multiply both numerator and denominator by$3-3i$

$\frac{5-i}{3+3i}\times \frac{3-3i}{3-3i}=\frac{(5-i)(3-3i)}{(3+3i)(3-3i)}$

and use the fact that

$(3+3i)(3-3i)={3}^{2}-{\left(3i\right)}^{2}=9-9{i}^{2}=9+9=18$

Then, expand the numerator as usual:

$(5-i)(3-3i)$

$=15-15i-3i+3{i}^{2}$

$=15-18i-3$

$12-18i$

We can simplify something:

$\frac{12-18i}{18}=\frac{2}{3}-i$

You must use something that resembles rationalization with roots at the denominator: multiply both numerator and denominator by

and use the fact that

Then, expand the numerator as usual:

We can simplify something: