Question

The value of \(\frac{5+5i}{3-4i} + \frac{20}{4+3i}\) is given by :

• A. \(3 - i\)
• B. \(1 + i\)
• C. \(\frac{5}{2} - \frac{i}{2}\)
• D. \(-2 + 9i\)

Hint:

To perform this faster:
Note that both denominators (\(3-4i\) and \(4+3i\)) have a modulus squared of 25.
We can write a common denominator of 25:
\[ \frac{5(1+i)(3+4i) + 20(4-3i)}{25} \]
\[ = \frac{5(-1+7i) + 80 - 60i}{25} = \frac{-5 + 35i + 80 - 60i}{25} = \frac{75 - 25i}{25} = 3 - i \]

Answer 1

The Correct Option is A