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

Answer:

$-\frac{6}{37} + \frac{371}{37}i$

Step-by-step explanation:

We need to evaluate $\frac{(5+6i)(5+6i)}{6+i}$

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

= $\frac{-11+60i}{6+i}$

Now we rationalize the denominator.

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

$\frac{-66 + 11i + 360i - 60i^2}{36 - i^2} = \frac{-66 + 60 + 371i}{37} = \frac{-6 + 371i}{37}$

= $-\frac{6}{37} + \frac{371}{37}i$

Formula used:

(a+b)² = a² + b² + 2ab

i² = -1