Question

Perform the operation and write the result in standard form 3i/3+i+8/3-i

Answer 1

2.7 + 1.7i

We require the fractions to have a common denominator.

multiply the numerator of the first fraction by (3 - i) and the numerator of the second fraction by (3 + 1)

= $\frac{3i(3-i)+8(3+i)}{(3+i)(3-i)}$

= $\frac{9i-3i^2+24+8i}{9-i^2}$

[ note that i² = ($\sqrt{(-1)^2}$ = - 1]

= $\frac{17i+27}{10}$ = 2.7 + 1.7i ← in standard form