Is this correct?

Question

Simplify: (4+5i)/(5-5i)

(A) (9i - 1)/(50)

(B) -(1)/(10) + (9i)/(10)

(C) ∅

(D) (4/5) - i

(E) None of the above

For this I got; (B) -(1)/(10) + (9i)/(10). Is this the correct answer?

Answer 1

To divide complex numbers we find the conjugate of the denominator and we multiply by that conjugate over itself. The conjugate is the expression with a swapped middle sign.

So the conjugate of the denominator (5 - 5i) is 5 + 5i so we multiply the expression by (5 + 5i) / (5 + 5i) as follows:

No simplifying by combining like terms and replacing i² with "-1", we get:

(-5 + 45i)/50 which can also be written as -1/10 + (9/10)i so "YES", you are correct!!

Answer 2

Yes, B is correct