Question

what are the values of x and y if this equation is true? 22(x + yi) + (28 + 4i) = 72 - 62i a. x = 3 and y = 2 b. x = 2 and y = -3 c. x = -3 and y = -2 d. x = 2 and y = 3

Explanation:

Step1: Expand the left-hand side

$22(x + yi) + (28 + 4i) = 22x + 22yi + 28 + 4i$

Step2: Group real and imaginary terms

$(22x + 28) + (22y + 4)i$

Step3: Equate real parts

$22x + 28 = 72$
Solve for $x$:
$22x = 72 - 28$
$22x = 44$
$x = \frac{44}{22} = 2$

Step4: Equate imaginary parts

$22y + 4 = -62$
Solve for $y$:
$22y = -62 - 4$
$22y = -66$
$y = \frac{-66}{22} = -3$

Answer:

B. $x = 2$ and $y = -3$