Question

2

Type the correct answer in each box.
What are the values of x and y that make the equations true?
Equation A
(x + yi) + (4 – 7i) = 3 – 4i
Equation B (t + yi) - (-6 + 14i) = 18 + 2i
In equation A, I =
and y =
.
In equation B, 1 =
and y =
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Answer 1

Answer: In equation A, -1 and 3 . In equation B, 12 and 16 .

picture below

Explanation:

Answer 2

Equation A: x = -1 and y = 3

Equation B: x = 12 and y = 16

Explanation:

In the complex numbers (a + bi) and (x + yi)

• (a + bi) + (x + yi) = (a + x) + (b + y)i

• (a + bi) - (x + yi) = (a - x) + (b - y)i

Equation A

∵ (x + yi) + (4 – 7i) = 3 – 4i

∴ (x + 4) + (y - 7)i = 3 - 4i

→ Compare the real parts and compare the imaginary parts

∴ x + 4 = 3 and y - 7 = -4

∵ x + 4 = 3

→ Subtract 4 from both sides

∴ x + 4 - 4 = 3 - 4

∴ x = -1

∵ y - 7 = -4

→ Add 7 to both sides

∴ y - 7 + 7 = -4 + 7

∴ y = 3

Equation B

∵ (x + yi) - (-6 + 14i) = 18 + 2i

∴ (x - -6) + (y - 14)i = 18 + 2i

→ (-)(-) = (+)

∴ (x + 6) + (y - 14)i = 18 + 2i

→ Compare the real parts and compare the imaginary parts

∴ x + 6 = 18 and y - 14 = 2

∵ x + 6 = 18

→ Subtract 6 from both sides

∴ x + 6 - 6 = 18 - 6

∴ x = 12

∵ y - 14 = 2

→ Add 14 to both sides

∴ y - 14 + 14 = 2 + 14

∴ y = 16