Question

. In the complex numbers, where i^2= -1. 2-i/-3+i F. -2/3 - i G. -5/8 + 1/8iH.-7/8 + 1/8iJ.-5/10 + 1/10iK. -7/10 + 1/10i

Answer 1

the given expression is,

`=(2-i)/(-3+i)`
`\begin{gathered} =(2-i)/(-3+i)*(-3-i)/(-3-i) \\ =((2-i)(-3-i))/((-3)^2-i^2) \end{gathered}`
`\begin{gathered} =(-6-2i+3i+i^2)/(9-(-1)) \\ =(-6+i-1)/(9+1) \\ =(-7+i)/(10) \end{gathered}`

so the answer is,

`=-(7)/(10)+(1i)/(10)`

we used

`(a+b)(a-b)=a^2-b^2`