Verified Answer :

Answer:

\(The\ simplified\ form\ of\ the\ \frac{5 + 6i}{4 + 6i}\ is\ \frac{56-6i}{52}.\)

Option (C) is correct .

Step-by-step explanation:

As the expression given in the question as follows.

\(= \frac{5 + 6i}{4 + 6i}\)

Now rationalize the expression.

\(= \frac{5 + 6i\times 4 - 6i}{4 + 6i\times 4 - 6i}\)

Using the formula

a² - b² = (a - b) (a + b)

Using in the above

\(= \frac{5 + 6i\times 4 - 6i}{(4)^{2} - (6i)^{2}}\)

\(= \frac{5\times 4-5\times 6i+6i\times 4-36\ i^{2}}{16 - 36(i)^{2}}\)

As i² = -1

\(= \frac{20-30i+24i+36}{16 + 36}\)

\(= \frac{56-6i}{52}\)

\(Therefore\ the\ simplified\ form\ of\ the\ \frac{5 + 6i}{4 + 6i}\ is\ \frac{56-6i}{52}.\)

Option (C) is correct .

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