How do you solve z( 3 + 2i) = (2 — 3i)?

1 Answer
Dec 29, 2015

z= i

Explanation:

z(3+2i) = (2-3i)

To solve for z divide both sides by 3+2i like this

(z(3+2i))/(3+2i) = (2-3i)/(3+2i)

=>z = (2-3i)/(3+2i)

Then multiply by the conjugate of the denominator to simplify the expression

z= ((2-3i)/(3+2i))*color(red)(((3-2i)/(3-2i))

Then multiply and combine like terms like this

z= (6-4i-9i+6i^2)/(9-6i+6i-4i^2)

=> (6 - 13i - +6i^2)/(9-4i^2)

Replace i^2 = -1 then simplify

=>z = (6 -13i +6*color(blue)(-1))/(9-4*color(blue)(-1))

=>z = (6-6-13i)/(9+4)

=>z = (-13 i)/(13) = i

z= i

I hope this helps :)