Answer
$\dfrac{5}{2}-\dfrac{7}{2}i$
Work Step by Step
Multiply the numerator and the denominator by the conjugate of $1-i$ which is $1+i$.
$\dfrac{6-i}{1+i}=\dfrac{6-i}{1+i}\cdot \dfrac{1-i}{1-i}$
Use FOIL method in the numerator and special formula $(a+b)(a-b)=a^2-b^2$ in the denominator.
$=\dfrac{6(1)-6(i)-1(i)+i^2}{1^2-i^2}$
$=\dfrac{6-6i-i+i^2}{1-i^2}$
Use $i^2=-1$.
$=\dfrac{6-6i-i+(-1)}{1-(-1)}$
$=\dfrac{6-6i-i-1}{1+1}$
Simplify.
$=\dfrac{5-7i}{2}$
$=\dfrac{5}{2}-\dfrac{7}{2}i$
Hence, the solution in the standard form is $\dfrac{5}{2}-\dfrac{7}{2}i$.
