select the correct answer.\nwhat are the values of x and y if this equation is true?\n$22(x + yi) + (28 +…

select the correct answer.\nwhat are the values of x and y if this equation is true?\n$22(x + yi) + (28 + 4i) = 72 - 62i$\na. $x = 2$ and $y = 3$\nb. $x = 3$ and $y = 2$\nc. $x = 2$ and $y = -3$\nd. $x = -3$ and $y = -2$

select the correct answer.\nwhat are the values of x and y if this equation is true?\n$22(x + yi) + (28 + 4i) = 72 - 62i$\na. $x = 2$ and $y = 3$\nb. $x = 3$ and $y = 2$\nc. $x = 2$ and $y = -3$\nd. $x = -3$ and $y = -2$

Answer

Explanation:

Step1: Expand the left-hand side

$22x + 22yi + 28 + 4i$

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:

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