How do you simplify 5−i3+3i?

Question

ocretz56 · Accepted Answer

Step 1
You must use something that resembles rationalization with roots at the denominator: multiply both numerator and denominator by

3 - 3 i

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

and use the fact that

(3 + 3 i) (3 - 3 i) = 3^{2} - {(3 i)}^{2} = 9 - 9 i^{2} = 9 + 9 = 18

Then, expand the numerator as usual:

(5 - i) (3 - 3 i)

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

= 15 - 18 i - 3

12 - 18 i

We can simplify something:

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

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