How do you simplify (3-7i) / (4i+2)3−7i4i+2?

1 Answer
Vikki
Dec 13, 2015

(3-7i)/(4i+2) = -1/9 -17/9 i 3−7i4i+2=−19−179i

Explanation:

Simplify " " (3-7i)/(4i+2) 3−7i4i+2

To simplify, we multiply by the conjugate of the denominator

((3-7i)/(4+2i))*color(red)(((4-2i)/(4-2i))(3−7i4+2i)⋅(4−2i4−2i)

Multiply, FOIL, distribute the expression

(12-6i -28i +14i^2)/(16- 8i +8i -2i^2)12−6i−28i+14i216−8i+8i−2i2

Combined like term, and replace color(blue)(i^2 = -1i2=−1

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

Simplify

(12-34i -14)/(16 +2)12−34i−1416+2

(-2 -34i)/(18) => (-2)/18 -(34i)/18−2−34i18⇒−218−34i18

-1/9 -17/9 i −19−179i

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