Question

Fraction with numerator as the square root of -25 and denominator as (5 - 2i) + (1 - 3i).

a.The quantity (-25 + 30i) divided by 61.
b.The quantity (-5 + 20i) divided by 17.
c.The quantity (25 + 30i) divided by 61.
d.The quantity (5 + 20i) divided by 17.

Answer 1

To simplify the given fraction with a square root of -25 in the numerator and a complex denominator, we need to rationalize the denominator and perform the division by multiplying both the numerator and denominator by the conjugate of the denominator.

Step-by-step explanation:

The given fraction has the numerator as the square root of -25 and the denominator as (5 - 2i) + (1 - 3i). To simplify, we need to rationalize the denominator and perform the division.

We can rationalize the denominator by multiplying both the numerator and denominator by the conjugate of the denominator, which is (5 - 2i) - (1 - 3i). This will eliminate the imaginary terms.

After multiplying and simplifying, the resulting fraction is option c. The quantity (25 + 30i) divided by 61.