# Chapter 1 - Section 1.3 - Complex Numbers - 1.3 Exercises - Page 103: 74

$-2+i$

#### Work Step by Step

Multiply the numerator and denominator by the conjugate of the complex imaginary number. $\frac{(-3+4i)}{(2-i)}\times\frac{(2+i)}{(2+i)}$ Use foil to expand numerator; use the difference of two squares to expand the denominator. $\frac{-6-3i+8i+4i^2}{4-i^2}$ Remember that $i^2=-1$. $\frac{-6+5i-4}{4+1}$ Combine like terms in both numerator and denominator. $\frac{-10+5i}{5}$ Divide each by 5. $-2+i$

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