Divide and simplify to the form $a+b i$.
-$\frac{4+3 i}{5+2 i}$
A) $\frac{14}{29}-\frac{23}{29} \mathrm{i}$
B) $\frac{26}{21}-\frac{1}{3} \mathrm{i}$
C) $\frac{26}{29}+\frac{7}{29} \mathrm{i}$
D) $\frac{2}{3}-\frac{1}{3} \mathrm{i}$

Question

Quizplus · Accepted Answer

To divide complex numbers, multiply the numerator and denominator by the complex conjugate of the denominator.$\frac{4+3 i}{5+2 i} = \frac{(4+3 i)(5-2 i)}{(5+2 i)(5-2 i)}$$\frac{(4+3 i)(5-2 i)}{(5+2 i)(5-2 i)} = \frac{20-8i+15i-6i^2}{25-4i^2}$$\frac{20-8i+15i-6i^2}{25-4i^2} = \frac{26+7i}{29}$$\frac{26+7i}{29} = \frac{26}{29}+\frac{7}{29} i$

Divide and Simplify to the Form a+bia+b ia+bi - 4+3i5+2i\frac{4+3 i}{5+2 i}5+2i4+3i​

Divide and Simplify to the Form $a+b i$
- $\frac{4+3 i}{5+2 i}$