Begin by observing the conjugate of 7 + i The conjugate has the same real part (7) in this case and the opposite sign for the complex part.
... The conjugate is 7 - i
The next thing to do is multiply the numerator and denominator by the confugate.
[tex]\text{...}\dfrac{-3 + i }{7 + i}*\dfrac{7 - i}{7 - i}[/tex]
You have 2 fractions that you must multiply together. You do it by numerator times numerator and denominator * denominator.
... numerator: (-3 + i) (7 - i ) = -21 + 3i + 7i - i^2 = -21 + 10i - i^2 = -21 + 10i + 1
... numerator: -20 + 10i
... denominator: (7 + i)(7 - i) = 49 - 7i + 7i - i^2 = 49 - i^2 = 50
Next you divide the numerator by the denominator.
[tex]\text{...}\dfrac{-20}{50} + \dfrac{10i}{50}[/tex] Reduce
[tex]\text{...}\dfrac{-2}{5} + \dfrac{i}{5}[/tex] Answer
