Worksheet: Equating, Adding, and Subtracting Complex Numbers

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In this worksheet, we will practice equating, adding, and subtracting complex numbers.

Q1:

Simplify 14−(9−8𝑖)+(3−12𝑖)−(9−4𝑖).

  • A 3 5 − 2 4 𝑖
  • B − 1
  • C 2 1 − 2 4 𝑖
  • D 3 − 1 6 𝑖

Q2:

If the complex numbers 4+5𝑖 and 𝑎+5𝑖 are equal, what is the value of 𝑎?

Q3:

If the complex numbers 7+𝑎𝑖 and 𝑏−3𝑖 are equal, what are the values of 𝑎 and 𝑏?

  • A 𝑎 = 3 , 𝑏 = − 7
  • B 𝑎 = − 3 , 𝑏 = − 7
  • C 𝑎 = 7 , 𝑏 = − 3
  • D 𝑎 = − 7 , 𝑏 = 3
  • E 𝑎 = − 3 , 𝑏 = 7

Q4:

What is (−7−𝑖)−(3−4𝑖)+(2−7𝑖)?

  • A − 2 − 1 2 𝑖
  • B − 6 + 2 𝑖
  • C − 1 2 + 1 0 𝑖
  • D − 8 − 4 𝑖

Q5:

What is −9+(7+4𝑖)+(−4−4𝑖)−(1+3𝑖)?

  • A 2 − 3 𝑖
  • B − 1 3 + 1 1 𝑖
  • C − 7 − 3 𝑖
  • D 1 2 + 1 1 𝑖
  • E 3 + 1 1 𝑖

Q6:

Find the real values of 𝑥 and 𝑦 that satisfy the equation (2𝑥−5)+𝑦𝑖=−3−5𝑖.

  • A 𝑥 = 1 , 𝑦 = 5
  • B 𝑥 = 1 , 𝑦 = − 5
  • C 𝑥 = − 3 , 𝑦 = − 5
  • D 𝑥 = 2 , 𝑦 = − 5

Q7:

Simplify (6−3𝑖)+(5−𝑖).

  • A − 4 + 1 1 𝑖
  • B 1 1 − 4 𝑖
  • C − 4 − 1 1 𝑖
  • D 1 1 + 4 𝑖

Q8:

Find the real values of 𝑥 and 𝑦 that satisfy the equation 𝑥+𝑦𝑖=10−7𝑖.

  • A 𝑥 = 1 0 , 𝑦 = − 7
  • B 𝑥 = 1 0 , 𝑦 = 7
  • C 𝑥 = − 7 , 𝑦 = 1 0
  • D 𝑥 = − 1 0 , 𝑦 = 7
  • E 𝑥 = − 1 0 , 𝑦 = − 7

Q9:

Simplify (6−𝑖)+(4−9𝑖).

  • A 1 0 + 1 0 𝑖
  • B 2 4 + 9 𝑖
  • C 1 0 − 1 0 𝑖
  • D 2 4 − 9 𝑖

Q10:

Simplify (4+𝑖)−(6+4𝑖).

  • A 2 + 3 𝑖
  • B − 2 + 3 𝑖
  • C 2 4 − 4 𝑖
  • D − 2 − 3 𝑖
  • E 2 4 + 4 𝑖

Q11:

Determine the real values of 𝑥 and 𝑦 that satisfy the equation 𝑥+𝑦𝑖=(−19+7𝑖)+(1−4𝑖).

  • A 𝑥 = − 1 9 , 𝑦 = − 2 8
  • B 𝑥 = − 2 0 , 𝑦 = 1 1
  • C 𝑥 = − 1 8 , 𝑦 = 3
  • D 𝑥 = 3 , 𝑦 = − 1 8

Q12:

Determine the real values of 𝑥 and 𝑦 that satisfy the equation 5𝑥+2+(3𝑦−5)𝑖=−3+4𝑖.

  • A 𝑥 = 1 , 𝑦 = − 3
  • B 𝑥 = 1 , 𝑦 = 3
  • C 𝑥 = − 1 , 𝑦 = − 3
  • D 𝑥 = − 1 , 𝑦 = 3

Q13:

Find the real values of 𝑥 and 𝑦 that satisfy the equation 4𝑥+2𝑦+(𝑥−𝑦)𝑖=8+8𝑖.

  • A 𝑥 = 4 , 𝑦 = − 4
  • B 𝑥 = − 4 , 𝑦 = 4
  • C 𝑥 = 4 , 𝑦 = 4
  • D 𝑥 = 8 , 𝑦 = 8

Q14:

Find the real values of 𝑥 and 𝑦 that satisfy the equation 2𝑥+2𝑥𝑖+4𝑦−4𝑦𝑖=8.

  • A 𝑥 = 2 , 𝑦 = − 1
  • B 𝑥 = − 2 , 𝑦 = − 1
  • C 𝑥 = 2 , 𝑦 = 1
  • D 𝑥 = 8 , 𝑦 = 0

Q15:

Evaluate (−4−5𝑖)−(2−6𝑖).

  • A − 6 − 1 1 𝑖
  • B − 6 + 𝑖
  • C − 2 − 1 1 𝑖
  • D 6 − 𝑖
  • E 2 + 1 1 𝑖

Q16:

If 𝑟=10+6𝑖 and 𝑠=4−3𝑖, find 𝑟−𝑠.

  • A − 1 4 − 3 𝑖
  • B − 6 − 9 𝑖
  • C 6 + 3 𝑖
  • D 1 4 + 3 𝑖
  • E 6 + 9 𝑖

Q17:

If 𝑟=5+2𝑖 and 𝑠=9−𝑖, find Re(𝑟−𝑠).

Q18:

If 𝑟=7−4𝑖 and 𝑠=2𝑖, express 𝑟−𝑠 in the form 𝑎+𝑏𝑖.

  • A 5 − 6 𝑖
  • B 5 − 4 𝑖
  • C 9 − 4 𝑖
  • D 7 − 6 𝑖
  • E 7 − 2 𝑖

Q19:

If 𝑟=2+3𝑖 and 𝑠=4−5𝑖, find 𝑟+𝑠.

  • A 6 − 2 𝑖
  • B 2 − 8 𝑖
  • C 6 − 8 𝑖
  • D − 2 + 8 𝑖
  • E 6 + 2 𝑖

Q20:

If 𝑎=7𝑖, 𝑏=−3−8𝑖, and 𝑐=4+5𝑖, is it true that (𝑎+𝑏)𝑖=𝑐+𝑏?

  • Ayes
  • Bno

Q21:

If 𝑟=2−𝑖 and 𝑠=−4+𝑖, what is the imaginary part of 𝑟+𝑠?

Q22:

Add 4−2𝑖 to 3+7𝑖.

  • A 1 − 9 𝑖
  • B 7 − 5 𝑖
  • C 7 + 5 𝑖
  • D − 1 + 9 𝑖
  • E 7 + 9 𝑖

Q23:

If 𝑟=4+3𝑖 and 𝑠=2−𝑖, find 𝑟+𝑠𝑖.

  • A 3 + 5 𝑖
  • B 4 + 4 𝑖
  • C − 2 + 6 𝑖
  • D 6 + 2 𝑖
  • E 5 + 5 𝑖

Q24:

Find the average of the complex numbers 4+5𝑖 and 8−5𝑖.

  • A4
  • B2
  • C6
  • D12
  • E16

Q25:

If 𝑟=−5+2𝑖 and 𝑠=−8−2𝑖, find 2𝑟+3𝑠.

  • A − 3 4 − 2 𝑖
  • B 3 4 + 2 𝑖
  • C − 3 4 + 2 𝑖
  • D 1 4 + 1 0 𝑖
  • E 1 + 1 0 𝑖

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