Question

Simplify the expression 5+6i/4+6i

A) 56-6i/-20
B) -16-6i/-20
C)56-6i/52
D) -16-6i/52

Answer 1

`The\ simplified\ form\ of\ the\ (5 + 6i)/(4 + 6i)\ is\ (56-6i)/(52).`

Option (C) is correct .

Explanation:

As the expression given in the question as follows.

`= (5 + 6i)/(4 + 6i)`

Now rationalize the expression.

`= (5 + 6i* 4 - 6i)/(4 + 6i* 4 - 6i)`

Using the formula

a² - b² = (a - b) (a + b)

Using in the above

`= (5 + 6i* 4 - 6i)/((4)^(2) - (6i)^(2))`

`= (5* 4-5* 6i+6i* 4-36\ i^(2))/(16 - 36(i)^(2))`

As i² = -1

`= (20-30i+24i+36)/(16 + 36)`

`= (56-6i)/(52)`

`Therefore\ the\ simplified\ form\ of\ the\ (5 + 6i)/(4 + 6i)\ is\ (56-6i)/(52).`

Option (C) is correct .