Question

Express $\frac{(-5-i)(-7+8i)}{(2-4i)}$ in the form of a complex number $a+bi$.

• A. $\frac{109}{10}-\frac{53}{10}i$
  
• B. $-\frac{109}{10}-\frac{53}{10}i$
  
• C. $\frac{109}{10}+\frac{53}{10}i$
  
• D. $-\frac{109}{10}+\frac{53}{10}i$
  

Answer 1

The correct option is C $\frac{109}{10}+\frac{53}{10}i$

We need to express $\frac{(-5-i)(-7+8i)}{(2-4i)}$ in the form of $a+bi$

On rationalising the given expression as follows:

$\frac{(-5-i)(-7+8i)(2+4i)}{(2-4i)(2+4i)}$

$=\frac{(35-40i+7i-8i^2)(2+4i)}{(4-16i^2)}$

$=\frac{(43-33i)(2+4i)}{(4+16)}$

$=\frac{(86+172i-66i-132i^2)}{20}$

$=\frac{(218+106i)}{20}$

$=\frac{109}{10}+\frac{53}{10}i$