What is (10+5i)/(2-i) ?

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

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simplify (10+5i)/(2-i)

simplify

\frac{10 + 5 i}{2 - i}

3 + 4 i

Solution steps

\frac{10 + 5 i}{2 - i}

Multiply by the conjugate

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

= \frac{( 10 + 5 i ) ( 2 + i )}{( 2 - i ) ( 2 + i )}

Simplify

\frac{( 10 + 5 i ) ( 2 + i )}{( 2 - i ) ( 2 + i )} : \frac{15 + 20 i}{5}

= \frac{15 + 20 i}{5}

Apply the fraction rule:

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

= \frac{15}{5} + \frac{20}{5} i

Simplify

\frac{15}{5} + \frac{20}{5} i : 3 + 4 i

= 3 + 4 i

85 - 4 x < 40

- x^{2} y^{2} + x^{4} + 9 y^{2} - 9 x^{2}

x^{3} + 6 x^{2} - 32

(4 - 4 i)^{2}

\frac{7}{2} x + 9 = x + \frac{13}{2}