# Chapter 10 - Section 10.7 - Complex Numbers - Exercise Set - Page 740: 68

$\dfrac{5}{3-2i}=\dfrac{15}{13}+\dfrac{10}{13}i$

#### Work Step by Step

$\dfrac{5}{3-2i}$ Multiply the numerator and the denominator of this expression by the complex conjugate of the denominator: $\dfrac{5}{3-2i}=\dfrac{5}{3-2i}\cdot\dfrac{3+2i}{3+2i}=\dfrac{5(3+2i)}{3^{2}-(2i)^{2}}=\dfrac{5(3+2i)}{9-4i^{2}}=...$ Substitute $i^{2}$ with $-1$ and simplify: $...=\dfrac{5(3+2i)}{9-4(-1)}=\dfrac{5(3+2i)}{9+4}=\dfrac{15+10i}{13}=\dfrac{15}{13}+\dfrac{10}{13}i$

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