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).

  • A35−24𝑖
  • B−1
  • C21−24𝑖
  • D3−16𝑖

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?

  • A𝑎=3, 𝑏=−7
  • B𝑎=−3, 𝑏=−7
  • C𝑎=7, 𝑏=−3
  • D𝑎=−7, 𝑏=3
  • E𝑎=−3, 𝑏=7

Q4:

What is (−7−𝑖)−(3−4𝑖)+(2−7𝑖)?

  • A−2−12𝑖
  • B−6+2𝑖
  • C−12+10𝑖
  • D−8−4𝑖

Q5:

What is −9+(7+4𝑖)+(−4−4𝑖)−(1+3𝑖)?

  • A2−3𝑖
  • B−13+11𝑖
  • C−7−3𝑖
  • D12+11𝑖
  • E3+11𝑖

Q6:

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

  • A𝑥=1, 𝑦=5
  • B𝑥=1, 𝑦=−5
  • C𝑥=−3, 𝑦=−5
  • D𝑥=2, 𝑦=−5

Q7:

Simplify (6−3𝑖)+(5−𝑖).

  • A−4+11𝑖
  • B11−4𝑖
  • C−4−11𝑖
  • D11+4𝑖

Q8:

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

  • A𝑥=10, 𝑦=−7
  • B𝑥=10, 𝑦=7
  • C𝑥=−7, 𝑦=10
  • D𝑥=−10, 𝑦=7
  • E𝑥=−10, 𝑦=−7

Q9:

Simplify (6−𝑖)+(4−9𝑖).

  • A10+10𝑖
  • B24+9𝑖
  • C10−10𝑖
  • D24−9𝑖

Q10:

Simplify (4+𝑖)−(6+4𝑖).

  • A2+3𝑖
  • B−2+3𝑖
  • C24−4𝑖
  • D−2−3𝑖
  • E24+4𝑖

Q11:

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

  • A𝑥=−19, 𝑦=−28
  • B𝑥=−20, 𝑦=11
  • C𝑥=−18, 𝑦=3
  • D𝑥=3, 𝑦=−18

Q12:

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

  • A𝑥=1, 𝑦=−3
  • B𝑥=1, 𝑦=3
  • C𝑥=−1, 𝑦=−3
  • D𝑥=−1, 𝑦=3

Q13:

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

  • A𝑥=4, 𝑦=−4
  • B𝑥=−4, 𝑦=4
  • C𝑥=4, 𝑦=4
  • D𝑥=8, 𝑦=8

Q14:

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

  • A𝑥=2, 𝑦=−1
  • B𝑥=−2, 𝑦=−1
  • C𝑥=2, 𝑦=1
  • D𝑥=8, 𝑦=0

Q15:

Evaluate (−4−5𝑖)−(2−6𝑖).

  • A−6−11𝑖
  • B−6+𝑖
  • C−2−11𝑖
  • D6−𝑖
  • E2+11𝑖

Q16:

If 𝑟=10+6𝑖 and 𝑠=4−3𝑖, find 𝑟−𝑠.

  • A−14−3𝑖
  • B−6−9𝑖
  • C6+3𝑖
  • D14+3𝑖
  • E6+9𝑖

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.

  • A5−6𝑖
  • B5−4𝑖
  • C9−4𝑖
  • D7−6𝑖
  • E7−2𝑖

Q19:

If 𝑟=2+3𝑖 and 𝑠=4−5𝑖, find 𝑟+𝑠.

  • A6−2𝑖
  • B2−8𝑖
  • C6−8𝑖
  • D−2+8𝑖
  • E6+2𝑖

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.

  • A1−9𝑖
  • B7−5𝑖
  • C7+5𝑖
  • D−1+9𝑖
  • E7+9𝑖

Q23:

If 𝑟=4+3𝑖 and 𝑠=2−𝑖, find 𝑟+𝑠𝑖.

  • A3+5𝑖
  • B4+4𝑖
  • C−2+6𝑖
  • D6+2𝑖
  • E5+5𝑖

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−34−2𝑖
  • B34+2𝑖
  • C−34+2𝑖
  • D14+10𝑖
  • E1+10𝑖

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