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

The solution to (3+2i)/((1-i)^2) is -1+i 3/2

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simplify (3+2i)/((1-i)^2)

simplify

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

- 1 + i \frac{3}{2}

Solution steps

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

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

= \frac{3 + 2 i}{- 2 i}

Apply the fraction rule:

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

= - \frac{3 + 2 i}{2 i}

Rationalize

- \frac{3 + 2 i}{2 i} : - \frac{2 - 3 i}{2}

= - \frac{2 - 3 i}{2}

Rewrite

- \frac{2 - 3 i}{2}

in standard complex form:

- 1 + \frac{3}{2} i

= - 1 + \frac{3}{2} i

(2 a + 2 y)^{2}

- 3 (x + 3)^{2}

- 11 + (- 9)

- x (7 x^{2} - 8 x - 3)