Worksheet: Equating, Adding, and Subtracting Complex Numbers

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

Q1:

Simplify 14(98𝑖)+(312𝑖)(94𝑖).

  • A3524𝑖
  • B1
  • C2124𝑖
  • D316𝑖

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 𝑏3𝑖 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 (7𝑖)(34𝑖)+(27𝑖)?

  • A212𝑖
  • B6+2𝑖
  • C12+10𝑖
  • D84𝑖

Q5:

What is 9+(7+4𝑖)+(44𝑖)(1+3𝑖)?

  • A23𝑖
  • B13+11𝑖
  • C73𝑖
  • D12+11𝑖
  • E3+11𝑖

Q6:

Find the real values of 𝑥 and 𝑦 that satisfy the equation (2𝑥5)+𝑦𝑖=35𝑖.

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

Q7:

Simplify (63𝑖)+(5𝑖).

  • A4+11𝑖
  • B114𝑖
  • C411𝑖
  • D11+4𝑖

Q8:

Find the real values of 𝑥 and 𝑦 that satisfy the equation 𝑥+𝑦𝑖=107𝑖.

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

Q9:

Simplify (6𝑖)+(49𝑖).

  • A10+10𝑖
  • B24+9𝑖
  • C1010𝑖
  • D249𝑖

Q10:

Simplify (4+𝑖)(6+4𝑖).

  • A2+3𝑖
  • B2+3𝑖
  • C244𝑖
  • D23𝑖
  • E24+4𝑖

Q11:

Determine the real values of 𝑥 and 𝑦 that satisfy the equation 𝑥+𝑦𝑖=(19+7𝑖)+(14𝑖).

  • 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+(3𝑦5)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+(𝑥𝑦)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+4𝑦4𝑦𝑖=8.

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

Q15:

Evaluate (45𝑖)(26𝑖).

  • A611𝑖
  • B6+𝑖
  • C211𝑖
  • D6𝑖
  • E2+11𝑖

Q16:

If 𝑟=10+6𝑖 and 𝑠=43𝑖, find 𝑟𝑠.

  • A143𝑖
  • B69𝑖
  • C6+3𝑖
  • D14+3𝑖
  • E6+9𝑖

Q17:

If 𝑟=5+2𝑖 and 𝑠=9𝑖, find Re(𝑟𝑠).

Q18:

If 𝑟=74𝑖 and 𝑠=2𝑖, express 𝑟𝑠 in the form 𝑎+𝑏𝑖.

  • A56𝑖
  • B54𝑖
  • C94𝑖
  • D76𝑖
  • E72𝑖

Q19:

If 𝑟=2+3𝑖 and 𝑠=45𝑖, find 𝑟+𝑠.

  • A62𝑖
  • B28𝑖
  • C68𝑖
  • D2+8𝑖
  • E6+2𝑖

Q20:

If 𝑎=7𝑖, 𝑏=38𝑖, and 𝑐=4+5𝑖, is it true that (𝑎+𝑏)𝑖=𝑐+𝑏?

  • Ayes
  • Bno

Q21:

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

Q22:

Add 42𝑖 to 3+7𝑖.

  • A19𝑖
  • B75𝑖
  • C7+5𝑖
  • D1+9𝑖
  • E7+9𝑖

Q23:

If 𝑟=4+3𝑖 and 𝑠=2𝑖, find 𝑟+𝑠𝑖.

  • A3+5𝑖
  • B4+4𝑖
  • C2+6𝑖
  • D6+2𝑖
  • E5+5𝑖

Q24:

Find the average of the complex numbers 4+5𝑖 and 85𝑖.

  • A4
  • B2
  • C6
  • D12
  • E16

Q25:

If 𝑟=5+2𝑖 and 𝑠=82𝑖, find 2𝑟+3𝑠.

  • A342𝑖
  • B34+2𝑖
  • C34+2𝑖
  • D14+10𝑖
  • E1+10𝑖

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