Question

Divide and simplify to the form a+bi. 5+6i 5+6i 6+ i (Simplify your answer. Type an integer or a fraction. Type your answer in the form a+bi.)

Answer 1

`-(6)/(37) + (371)/(37)i`

Explanation:

We need to evaluate
`((5+6i)(5+6i))/(6+i)`

(5+6i)(5+6i) = (25 + 36i² + 60i) = (25 - 36 + 60i) = -11 + 60i

=
`(-11+60i)/(6+i)`

Now we rationalize the denominator.

Now, multiplying both the numerator and denominator by (6-i)

`(-66 + 11i + 360i - 60i^2)/(36 - i^2) = (-66 + 60  + 371i)/(37) = (-6 + 371i)/(37)`

=
`-(6)/(37) + (371)/(37)i`

Formula used:

(a+b)² = a² + b² + 2ab

i² = -1