How do you divide #( 4 + 3i) /( 7 + i)#?

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Answer 1 · 2016-01-26T21:03:43

#31/50+17/50i#

In order to make the denominator not contain complex numbers, multiply the fraction by the complex conjugate of the denominator.

#=(4+3i)/(7+i)((7-i)/(7-i))#

Distribute each of these.

#=(28+17i-3i^2)/(49-i^2)#

We can simplify this further, since #i^2=-1#.

#=(28+17i-3(-1))/(49-(-1))#

#=(28+17i+3)/(49+1)#

#=(31+17i)/50#

Complex numbers are typically written in #a+bi# form.

#=31/50+17/50i#