Question

find the values of x and y that make this equation true.
-4 + 13i = 2x - 8 + (3y + 4)i

x =

y =

Explanation:

Step1: Equate real parts

For complex numbers \( a + bi = c + di \), \( a = c \) and \( b = d \). Real parts: \(-4 = 2x - 8\).
Solve: \( 2x = -4 + 8 = 4 \), so \( x = \frac{4}{2} = 2 \).

Step2: Equate imaginary parts

Imaginary parts: \( 13 = 3y + 4 \).
Solve: \( 3y = 13 - 4 = 9 \), so \( y = \frac{9}{3} = 3 \).

Answer:

\( x = 2 \), \( y = 3 \)