Answer
$\frac{7-24i}{25}$
Work Step by Step
Step 1: Multiplying both the numerator and the denominator of the expression by the complex conjugate of the denominator:
$\frac{4-3i}{4+3i}\times\frac{4-3i}{4-3i}$
Step 2: $\frac{4-3i}{4+3i}\times\frac{4-3i}{4-3i}=\frac{(4-3i)(4-3i)}{(4)^{2}-(3i)^{2}}$
Step 3: $\frac{(4-3i)(4-3i)}{(4)^{2}-(3i)^{2}}=\frac{16-12i-12i+9i^{2}}{16-9i^{2}}=\frac{16-24i+9(-1)}{16-9(-1)}$
Step 4: $\frac{16-24i+9(-1)}{16-9(-1)}=\frac{16-24i-9}{25}=\frac{7-24i}{25}$
