How do you simplify #(3-7i) / (4i+2)#?

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Answer 1 · 2015-12-13T00:56:06

#(3-7i)/(4i+2) = -1/9 -17/9 i #

Simplify #" " (3-7i)/(4i+2)#

To simplify, we multiply by the conjugate of the denominator

#((3-7i)/(4+2i))*color(red)(((4-2i)/(4-2i))#

Multiply, FOIL, distribute the expression

#(12-6i -28i +14i^2)/(16- 8i +8i -2i^2)#

Combined like term, and replace #color(blue)(i^2 = -1#

#(12-34i +14color(blue)((-1)))/(16 - 2color(blue)((-1))#

Simplify

#(12-34i -14)/(16 +2)#

#(-2 -34i)/(18) => (-2)/18 -(34i)/18#

#-1/9 -17/9 i #