What is simplify-(4+7i)/((1-i)i) ?

The solution to simplify-(4+7i)/((1-i)i) is -11/2-i 3/2

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simplify-(4+7i)/((1-i)i)

simplify

- \frac{4 + 7 i}{( 1 - i ) i}

- \frac{11}{2} - i \frac{3}{2}

Solution steps

- \frac{4 + 7 i}{( 1 - i ) i}

(1 - i) i : 1 + i

= - \frac{4 + 7 i}{1 + i}

Apply complex arithmetic rule:

\frac{a + bi}{c + d i} = \frac{( c - d i ) ( a + bi )}{( c - d i ) ( c + d i )} = \frac{( a c + b d ) + ( b c - a d ) i}{c ^{2} + d ^{2}}

a = 4, b = 7, c = 1, d = 1

= - \frac{( 4 \cdot 1 + 7 \cdot 1 ) + ( 7 \cdot 1 - 4 \cdot 1 ) i}{1 ^{2} + 1 ^{2}}

Refine

= - \frac{11 + 3 i}{2}

Rewrite

- \frac{11 + 3 i}{2}

in standard complex form:

- \frac{11}{2} - \frac{3}{2} i

= - \frac{11}{2} - \frac{3}{2} i

- 8 (5 - 3 v)

(x - 3) (3 x - 4)

100 \cdot 4

- 38

2 x (3 x + 4) - 5

What is simplify-(4+7i)/((1-i)i) ?
The solution to simplify-(4+7i)/((1-i)i) is -11/2-i 3/2