Explained: "How do you simplify −9−9i÷−1−8i?"

Jean Blumer

Answered question

2022-01-18

How do you simplify

- 9 - 9 i \div - 1 - 8 i

mauricio0815sh

Beginner2022-01-19Added 34 answers

- 9 - 9 i \div - 1 - 8 i = \frac{81}{65} - \frac{63}{65} i

Explanation:

- 9 - 9 i \div - 1 - 8 i = \frac{- 9 - 9 i}{- 1 - 8 i}

= \frac{- 9 - 9 i}{- 1 - 8 i} \cdot \frac{- 1 + 8 i}{- 1 + 8 i}

\frac{9 + 9 i - 72 i + 72}{1 + 64}

= \frac{81 - 63 i}{65}

Carl Swisher

Beginner2022-01-20Added 28 answers

Solution:

- 9 - 9 i \div - 1 - 8 i

can be written as

\frac{- 9 - 9 i}{- 1 - 8 i}

To simplify we need to multiply numerator and denominator by the complex conjugate of the denominator.
Complex conjugate of a number

a + b i is a - b i

hence in above case one needs to multiply by

- 1 + 8 i

Hence

\frac{- 9 - 9 i}{- 1 - 8 i}

= \frac{(- 9 - 9 i) \times (- 1 + 8 i)}{(- 1 - 8 i) \times (- 1 + 8 i)}

= \frac{9 - 72 i + 9 i - 72 i^{2}}{{(- 1)}^{2} - {(8 i)}^{2}}

= \frac{9 - 72 i + 9 i - 72 (- 1)}{1 - 64 (- 1)}

= \frac{9 - 72 i + 9 i + 72}{1 + 64}

= \frac{81 - 63 i}{65}

= \frac{81}{65} - \frac{63}{65} i

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