rationalize the denominator: $\frac{7 + 5i}{-7i}$\na $\frac{-5 + 7i}{10}$\nb $\frac{35 - 7i}{7}$\nc…

rationalize the denominator: $\frac{7 + 5i}{-7i}$\na $\frac{-5 + 7i}{10}$\nb $\frac{35 - 7i}{7}$\nc $\frac{-5 + 7i}{7}$\nd $\frac{35 - 7i}{10}$

rationalize the denominator: $\frac{7 + 5i}{-7i}$\na $\frac{-5 + 7i}{10}$\nb $\frac{35 - 7i}{7}$\nc $\frac{-5 + 7i}{7}$\nd $\frac{35 - 7i}{10}$

Answer

Answer:

C. $\frac{- 5 + 7i}{7}$

Explanation:

Step1: Multiply by conjugate

Multiply numerator and denominator by $i$. $\frac{(7 + 5i)\times i}{-7i\times i}$

Step2: Expand numerator and denominator

Use distributive property and $i^2=-1$. Numerator: $(7 + 5i)\times i=7i+5i^2=7i - 5$. Denominator: $-7i\times i=-7i^2 = 7$. So the fraction is $\frac{-5 + 7i}{7}$.