Question

What is the quotient of the complex number 4-3i divided by its conjugate?

Answer 1

Answer: C. $\frac{7}{25}-\frac{24}{25}i$

Step-by-step explanation:

1. You have the following division:

$\frac{4-3i}{4+3i}$ (As you can see, to find the conjugate of  4-3i you must change the sign between the terms).

2. To solve this division, you must multiply the numerator and the denominator by the conjugate of the denominator, as following:

$=\frac{(4-3i)}{(4+3i)}\frac{(4-3i)}{(4-3i)}=\frac{16-12i-12i+9i^{2}}{16-9i^{2}}$

3. Keeping on mind that $i^{2}=-1$, you have:

$=\frac{16-12i-12i+9(-1)}{16-9(-1)}$

4. Simplifying:

$=\frac{7-24i}{25}=\frac{7}{25}-\frac{24}{25}i$

5. The result is:

$\frac{7}{25}-\frac{24}{25}i$