How do you divide (5/(1+i))(51+i)?

3 Answers
Jul 28, 2018

1/2(5-5i)12(55i)

Explanation:

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

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

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

=(5-5i)/(1-i^2)toi^2=-1=55i1i2i2=1

=(5-5i)/2=1/2(5-5i)=55i2=12(55i)

5/2(1-i)52(1i)

Explanation:

Given that

5/{1+i}51+i

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

={5(1-i)}/{1^2-i^2}=5(1i)12i2

={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!