Question

Divide the following complex numbers: (3+i)/(2-3i)

Answer 1

Answer:

B

Step-by-step explanation:

To divide the fraction, multiply the numerator and denominator by the complex conjugate of the denominator.

The conjugate of 2 - 3i is 2 + 3i, thus

= $\frac{(3+i)(2+3i)}{(2-3i)(2+3i)}$

Expand numerator/ denominator using FOIL

= $\frac{6+11i+3i^2}{4-9i^2}$ → note i² = - 1

= $\frac{6+11i-3}{4+9}$

= $\frac{3+11i}{13}$

= $\frac{3}{13}$ + $\frac{11}{13}$ i → B