Question #189e8

1 Answer
sente
Oct 19, 2016

#(3i)/(4+2i)=3/10 + 3/5i#

Explanation:

The complex conjugate or conjugate of a complex number #a+bi#, denoted #bar(a+bi)#, is given by

#bar(a+bi) = a-bi#

A useful property of the complex conjugate is that for any complex number #z#, we have #zbar(z) in RR#, that is, the product of a complex number and is conjugate is real.

We use this property by multiplying the numerator and denominator of the expression by the conjugate of the denominator. This results in a real-valued denominator when we can then distribute (if necessary).

#(3i)/(4+2i) = (3i(4-2i))/((4+2i)(4-2i))#

#=(12i-6i^2)/(16+8i-8i-4i^2)#

#=(12i-(-6))/(16-(-4))#

#=(6+12i)/20#

#=3/10 + 3/5i#

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