How do you divide #4+2i div 3-i#?

2 Answers
Daniel L.
Dec 29, 2015

The result is #1+i#

Explanation:

To perform the division of complex numbers you have to expand the fraction by the complex conjugate of the denominator. After doing this you get a real number in the denominator.

#(4+2i)/(3-i)=((4+2i)(3+i))/((3-i)(3+i))=(10+10i)/10=1+i#

SagarStudy
Dec 29, 2015

#1+i#

Explanation:

#(4+2i)/(3-i)#
Multiply and divide by the conjugate of the expression present in denominator i.e #3+i#.
#implies (4+2i)/(3-i)=(4+2i)/(3-i)*(3+i)/(3+i)=(12+4i+6i+2i^2)/((3)^2-(i)^2)#
#=(12+10i-2)/(9-(-1))=(10+10i)/(9+1)=(10(1+i))/10=1+i#
Hence the answer is #1+i#.

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