What is (40+30i)/((i-2)(1-3i)) ?

The solution to (40+30i)/((i-2)(1-3i)) is 5-5i

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simplify (40+30i)/((i-2)(1-3i))

simplify

\frac{40 + 30 i}{( i - 2 ) ( 1 - 3 i )}

5 - 5 i

Solution steps

\frac{40 + 30 i}{( i - 2 ) ( 1 - 3 i )}

Simplify

(i - 2) (1 - 3 i) : 1 + 7 i

= \frac{40 + 30 i}{1 + 7 i}

Multiply by the conjugate

\frac{1 - 7 i}{1 - 7 i}

= \frac{( 40 + 30 i ) ( 1 - 7 i )}{( 1 + 7 i ) ( 1 - 7 i )}

Simplify

\frac{( 40 + 30 i ) ( 1 - 7 i )}{( 1 + 7 i ) ( 1 - 7 i )} : \frac{250 - 250 i}{50}

= \frac{250 - 250 i}{50}

Apply the fraction rule:

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

= \frac{250}{50} + \frac{- 250}{50} i

Simplify

\frac{250}{50} + \frac{- 250}{50} i : 5 - 5 i

= 5 - 5 i

\frac{0.1}{1 - 0.1}

\frac{3}{7} \div \frac{4}{5}

(- 1) - (- 4)

34 a x^{2} + 51 a^{(2)} y - 68 a y^{2}

k^{2} - 2 k + 1