Question

Find the values of x and y that satisfy the equation –21 + 5yi = 7x – 10i.

Answer 1

The values of x and y are x = -3 and y = -2

Explanation:

In the complex numbers if a + bi = c + di, then the real parts are equal and the imaginary parts are equal

• a = c

• b = d

Let us use this rule to solve the question

∵ -21 + 5yi = 7x - 10i

∴ The real parts are -21 and 7x

∴ The imaginary parts are 5y and -10

∵ The real parts are equal

∴ 7x = -21

→ Divide both sides by 7

∴
`(7x)/(7)` =
`(-21)/(7)`

∴ x = -3

∵ The imaginary parts are equal

∴ 5y = -10

→ Divide both sides by 5

∴
`(5y)/(5)` =
`(-10)/(5)`

∴ y = -2

∴ The values of x and y are x = -3 and y = -2