What is (1-5i)/(4+4i)-1/i ?

The solution to (1-5i)/(4+4i)-1/i is -1/2+1/4 i

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simplify (1-5i)/(4+4i)-1/i

simplify

\frac{1 - 5 i}{4 + 4 i} - \frac{1}{i}

- \frac{1}{2} + \frac{1}{4} i

Solution steps

\frac{1 - 5 i}{4 + 4 i} - \frac{1}{i}

\frac{1 - 5 i}{4 + 4 i} = - \frac{2 + 3 i}{4}

\frac{1}{i} = - i

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

Apply rule:

a - (- b) = a + b

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

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

Join

- \frac{2 + 3 i}{4} + i : \frac{i - 2}{4}

= \frac{i - 2}{4}

Rewrite

i - 2

in standard complex form:

- 2 + i

= \frac{- 2 + i}{4}

Apply the fraction rule:

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

= \frac{- 2}{4} + \frac{1}{4} i

Cancel

\frac{- 2}{4} : - \frac{1}{2}

= - \frac{1}{2} + \frac{1}{4} i

9 x^{2} + 6 x = - 5

(x + 2)^{2} - 28 = 0

\frac{x - 1}{- 4} = - 6

x^{2} + 8 a x - 9 a^{2}

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