Solve (3-2i)(2+3i)/(1+2i)(2-i) - ScanMath

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Type your math problem... (3-2i)(2+3i)/(1+2i)(2-i)

Question

Simplify the expression

5 - 12 i

Evaluate

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

Divide the terms

More Steps

(3 - 2 i) (\frac{8}{5} - \frac{1}{5} i) (2 - i)

Multiply the first two terms

More Steps

(\frac{22}{5} - \frac{19}{5} i) (2 - i)

Apply the distributive property

\frac{22}{5} \times 2 + \frac{22}{5} (- i) - \frac{19}{5} i \times 2 - \frac{19}{5} i (- i)

Multiply the numbers

More Steps

\frac{44}{5} + \frac{22}{5} (- i) - \frac{19}{5} i \times 2 - \frac{19}{5} i (- i)

Multiply the numbers

\frac{44}{5} - \frac{22}{5} i - \frac{19}{5} i \times 2 - \frac{19}{5} i (- i)

Multiply the numbers

\frac{44}{5} - \frac{22}{5} i - \frac{38}{5} i - \frac{19}{5} i (- i)

Multiply the numbers

More Steps

\frac{44}{5} - \frac{22}{5} i - \frac{38}{5} i - \frac{19}{5}

Subtract the numbers

More Steps

\frac{44}{5} - 12 i - \frac{19}{5}

Reduce fractions to a common denominator

\frac{44}{5} + \frac{- 12 i \times 5}{5} - \frac{19}{5}

Write all numerators above the common denominator

\frac{44 - 12 i \times 5 - 19}{5}

Multiply the terms

\frac{44 - 60 i - 19}{5}

Calculate

\frac{25 - 60 i}{5}

Rewrite the expression

\frac{5 ( 5 - 12 i )}{5}

Solution

5 - 12 i

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