What is ((5+2i))/((2+9i))(10+12i) ?

The solution to ((5+2i))/((2+9i))(10+12i) is 772/85-74/85 i

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simplify ((5+2i))/((2+9i))(10+12i)

simplify

\frac{( 5 + 2 i )}{( 2 + 9 i )} (10 + 12 i)

\frac{772}{85} - \frac{74}{85} i

Solution steps

\frac{5 + 2 i}{2 + 9 i} (10 + 12 i)

Simplify

\frac{5 + 2 i}{2 + 9 i} : \frac{28}{85} - \frac{41}{85} i

= (\frac{28}{85} - \frac{41}{85} i) (10 + 12 i)

Apply complex arithmetic rule:

(a + bi) (c + d i) = (a c - b d) + (a d + b c) i

= (\frac{28}{85} \cdot 10 - (- \frac{41}{85}) \cdot 12) + (\frac{28}{85} \cdot 12 - \frac{41}{85} \cdot 10) i

Simplify

(\frac{28}{85} \cdot 10 - (- \frac{41}{85}) \cdot 12) + (\frac{28}{85} \cdot 12 - \frac{41}{85} \cdot 10) i : \frac{772}{85} - \frac{74}{85} i

= \frac{772}{85} - \frac{74}{85} i

\frac{10}{10000}

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What is ((5+2i))/((2+9i))(10+12i) ?
The solution to ((5+2i))/((2+9i))(10+12i) is 772/85-74/85 i