Answer:
[tex]-\frac{6}{37} + \frac{371}{37}i[/tex]
Step-by-step explanation:
We need to evaluate [tex]\frac{(5+6i)(5+6i)}{6+i}[/tex]
(5+6i)(5+6i) = (25 + 36i² + 60i) = (25 - 36 + 60i) = -11 + 60i
= [tex]\frac{-11+60i}{6+i}[/tex]
Now we rationalize the denominator.
Now, multiplying both the numerator and denominator by (6-i)
[tex]\frac{-66 + 11i + 360i - 60i^2}{36 - i^2} = \frac{-66 + 60 + 371i}{37} = \frac{-6 + 371i}{37}[/tex]
= [tex]-\frac{6}{37} + \frac{371}{37}i[/tex]
Formula used:
(a+b)² = a² + b² + 2ab
i² = -1
