Question

find the values of x and y that make this equation true,
-8 + 11i = 2x + 2 + (3y + 5)i

x =

y =

Explanation:

Step1: Equate real parts

For complex numbers \(a + bi = c + di\), real parts \(a = c\) and imaginary parts \(b = d\). Here, real parts: \(-8 = 2x + 2\)
Solve for \(x\):
\(2x = -8 - 2\)
\(2x = -10\)
\(x = \frac{-10}{2} = -5\)

Step2: Equate imaginary parts

Imaginary parts: \(11 = 3y + 5\)
Solve for \(y\):
\(3y = 11 - 5\)
\(3y = 6\)
\(y = \frac{6}{3} = 2\)

Answer:

\(x = -5\), \(y = 2\)