Question

How do you simplify `-9-9i div -1-8i`?

Answer 1

`-9-9idiv-1-8i= color(green)(81/65-63/65i)`

Explanation:

`-9-9i div -1-8i = (-9-9i)/(-1-8i)`

`color(white)("XXX")=(-9-9i)/(-1-8i)*(-1+8i)/(-1+8i)`

`color(white)("XXX")(9+9i-72i+72)/(1+64)`

`color(white)("XXX")=(81-63i)/65`

Answer 2

`−9−9i div −1−8i=81/65-63/65i`

Explanation:

`−9−9i div −1−8i` can be written as `(−9−9i)/(−1−8i)`

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

Complex conjugate of a number `a+bi` is `a-bi`,

hence in above case one needs to multiply by `-1+8i`

Hence `(−9−9i)/(−1−8i)`

= `((−9−9i)xx(-1+8i))/((−1−8i)xx(-1+8i))`

= `(9-72i+9i-72i^2)/((-1)^2-(8i)^2)`

= `(9-72i+9i-72(-1))/(1-64(-1))`

= `(9-72i+9i+72)/(1+64)`

= `(81-63i)/65`

= `81/65-63/65i`