Answer:
[tex]The\ simplified\ form\ of\ the\ \frac{5 + 6i}{4 + 6i}\ is\ \frac{56-6i}{52}.[/tex]
Option (C) is correct .
Step-by-step explanation:
As the expression given in the question as follows.
[tex]= \frac{5 + 6i}{4 + 6i}[/tex]
Now rationalize the expression.
[tex]= \frac{5 + 6i\times 4 - 6i}{4 + 6i\times 4 - 6i}[/tex]
Using the formula
a² - b² = (a - b) (a + b)
Using in the above
[tex]= \frac{5 + 6i\times 4 - 6i}{(4)^{2} - (6i)^{2}}[/tex]
[tex]= \frac{5\times 4-5\times 6i+6i\times 4-36\ i^{2}}{16 - 36(i)^{2}}[/tex]
As i² = -1
[tex]= \frac{20-30i+24i+36}{16 + 36}[/tex]
[tex]= \frac{56-6i}{52}[/tex]
[tex]Therefore\ the\ simplified\ form\ of\ the\ \frac{5 + 6i}{4 + 6i}\ is\ \frac{56-6i}{52}.[/tex]
Option (C) is correct .
