Question

determine x and y such that: (2+3i) (x+yi) = -7+3i

Answer 1

Step-by-step explanation:

(2+3i)(x+yi) = -7+3i

x+yi = (-7+3i)/ (2+3i)

multiple right by 2-3i in numerator and denominator

x+yi = (-7+3i)(2-3i) / (2+3i)(2-3i)

x+yi = (-14+21i +6i - 9i²)/ (2-9i²)

as we know i² = -1

hence,

x+yi = (-14 +9 +27i )/(2+9)

x+yi = (-5+27i)/11

x+yi = -5/11 +27i/11

comparing both sides we get

x= -5/11 = -0.45

y = 27/11= 2.45