Question

Simplify  (−3 + i) / (7+i)

Answer 1

Answer: -2/5+1/5i

Explanation:

complex rule.

(-3*7+1*1)+(1*7-(-3)*1)i/7²+1² ← as the fractions

then refine and rewrite the problem down.

-20+10i/50 ← as the fractions shown.

-20+10i/50=-2+i/5

you can also rewrite the problem down in standard complex form.

-2+i/5=-2/5+1/5i

=-2/5+1/5i

Hope this helps!

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Answer 2

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.

$\text{...}\dfrac{-3 + i }{7 + i}*\dfrac{7 - i}{7 - i}$

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.

$\text{...}\dfrac{-20}{50} + \dfrac{10i}{50}$      Reduce

$\text{...}\dfrac{-2}{5} + \dfrac{i}{5}$                 Answer