How do you divide (5/(1+i))?

3 Answers
Jul 28, 2018

1/2(5-5i)

Explanation:

"multiply the numerator/denominator by the complex"
"conjugate of the denominator"

"the conjugate of "1+i" is "1color(red)(-)i

=(5(1-i))/((1+i)(1-i))

=(5-5i)/(1-i^2)toi^2=-1

=(5-5i)/2=1/2(5-5i)

5/2(1-i)

Explanation:

Given that

5/{1+i}

={5(1-i)}/{(1+i)(1-i)}

={5(1-i)}/{1^2-i^2}

={5(1-i)}/{1-(-1)}\quad (\because \ i^2=-1)

={5(1-i)}/2

=5/2(1-i)

Jul 28, 2018

5/2(1-i)

Explanation:

Dividing by complex numbers is the same as multiplying by the complex conjugate:

Complex Conjugate of a complex number a+bi is a-bi.

Multiplying by the complex conjugate, we now have

(5(1-i))/((1+i)(1-i))

(5(1-i))/(1-i^2)

Recall that i^2=-1. This all simplifies to

5/2(1-i)

Hope this helps!