Question

find the values of x and y that satisfy the equation.
3x + 6i = 27 + yi
x = \square and y = \square

Explanation:

Step1: Equate real parts

For complex numbers \(a + bi = c + di\), real parts \(a = c\) and imaginary parts \(b = d\). Here, real part of left: \(3x\), real part of right: \(27\). So \(3x = 27\).

Step2: Solve for \(x\)

Divide both sides by 3: \(x=\frac{27}{3}=9\).

Step3: Equate imaginary parts

Imaginary part of left: \(6\), imaginary part of right: \(y\). So \(y = 6\).

Answer:

\(x = 9\) and \(y = 6\)