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

3 Answers
Jim G.
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)#

Harish Chandra Rajpoot
Jul 28, 2018

#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)#

Jacobi J.
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!

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