What is (10+15i)/((1-i)^2) ?

The solution to (10+15i)/((1-i)^2) is -15/2+5i

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simplify (10+15i)/((1-i)^2)

simplify

\frac{10 + 15 i}{( 1 - i ) ^{2}}

- \frac{15}{2} + 5 i

Solution steps

\frac{10 + 15 i}{( 1 - i ) ^{2}}

(1 - i)^{2} = - 2 i

= \frac{10 + 15 i}{- 2 i}

Apply the fraction rule:

\frac{a}{- b} = - \frac{a}{b}

= - \frac{10 + 15 i}{2 i}

Rationalize

- \frac{10 + 15 i}{2 i} : - \frac{15 - 10 i}{2}

= - \frac{15 - 10 i}{2}

Rewrite

- \frac{15 - 10 i}{2}

in standard complex form:

- \frac{15}{2} + 5 i

= - \frac{15}{2} + 5 i

(x^{1})^{2}

\frac{2}{6} \cdot \frac{3}{5}

15 - 660

\frac{u ^{4} - 1}{u ^{3} - 1}

(2 x^{2} + 3 x)^{2}