What is ((1+3i)(-3-i))/(2-2i) ?

The solution to ((1+3i)(-3-i))/(2-2i) is 5/2-5/2 i

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simplify ((1+3i)(-3-i))/(2-2i)

simplify

\frac{( 1 + 3 i ) ( - 3 - i )}{2 - 2 i}

\frac{5}{2} - \frac{5}{2} i

Solution steps

\frac{( 1 + 3 i ) ( - 3 - i )}{2 - 2 i}

Multiply by the conjugate

\frac{2 + 2 i}{2 + 2 i}

= \frac{( 1 + 3 i ) ( - 3 - i ) ( 2 + 2 i )}{( 2 - 2 i ) ( 2 + 2 i )}

Simplify

\frac{( 1 + 3 i ) ( - 3 - i ) ( 2 + 2 i )}{( 2 - 2 i ) ( 2 + 2 i )} : \frac{20 - 20 i}{8}

= \frac{20 - 20 i}{8}

Apply the fraction rule:

\frac{a + bi}{c} = \frac{a}{c} + \frac{b}{c} i

= \frac{20}{8} + \frac{- 20}{8} i

Simplify

\frac{20}{8} + \frac{- 20}{8} i : \frac{5}{2} - \frac{5}{2} i

= \frac{5}{2} - \frac{5}{2} i

∣ 54 ∣

4 \cdot (- 10)

\frac{2 x ^{2} + 5 x - 3}{1 - 2 x}

(- 2 x + 5 y)^{4}

5 x^{2} + 7 x^{2}

What is ((1+3i)(-3-i))/(2-2i) ?
The solution to ((1+3i)(-3-i))/(2-2i) is 5/2-5/2 i