Answer to Question #218558 in Calculus for Unknown346307

Question

6.

Find the values of a and b, where a and b are real, given that (a + bi)(2 – i) = 5 – i.

Answer 1

$$(a+bi)(2-i)=2a-ai+2bi+b$$

$$=(2a+b)+(-a+2b)i=5-i$$

$$\begin{matrix} 2a+b=5\\ -a+2b=-1 \end{matrix}$$

$$\begin{matrix} b=-2a+5\\ -a-4a+10=-1 \end{matrix}$$

$$\begin{matrix} a=2.2\\ b=0.6 \end{matrix}$$