What is ((3-4i)(4-3i))/(2-i) ?

The solution to ((3-4i)(4-3i))/(2-i) is 5-10i

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simplify ((3-4i)(4-3i))/(2-i)

simplify

\frac{( 3 - 4 i ) ( 4 - 3 i )}{2 - i}

5 - 10 i

Solution steps

\frac{( 3 - 4 i ) ( 4 - 3 i )}{2 - i}

Multiply by the conjugate

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

= \frac{( 3 - 4 i ) ( 4 - 3 i ) ( 2 + i )}{( 2 - i ) ( 2 + i )}

Simplify

\frac{( 3 - 4 i ) ( 4 - 3 i ) ( 2 + i )}{( 2 - i ) ( 2 + i )} : \frac{25 - 50 i}{5}

= \frac{25 - 50 i}{5}

Apply the fraction rule:

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

= \frac{25}{5} + \frac{- 50}{5} i

Simplify

\frac{25}{5} + \frac{- 50}{5} i : 5 - 10 i

= 5 - 10 i

(x + 2) (y + 3)

\frac{1}{8} + \frac{3}{7}

\frac{625}{2}

(2 k + 3) (k - 1)

sin^{2} (θ) cot^{2} (θ)