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Worksheet: Equating, Adding, and Subtracting Complex Numbers

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

Q1:

What is ( βˆ’ 7 βˆ’ 𝑖 ) βˆ’ ( 3 βˆ’ 4 𝑖 ) + ( 2 βˆ’ 7 𝑖 ) ?

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

Q2:

Simplify 1 4 βˆ’ ( 9 βˆ’ 8 𝑖 ) + ( 3 βˆ’ 1 2 𝑖 ) βˆ’ ( 9 βˆ’ 4 𝑖 ) .

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

Q3:

Find the real values of π‘₯ and 𝑦 that satisfy the equation ( 2 π‘₯ βˆ’ 5 ) + 𝑦 𝑖 = βˆ’ 3 βˆ’ 5 𝑖 .

  • A π‘₯ = 2 , 𝑦 = βˆ’ 5
  • B π‘₯ = 1 , 𝑦 = 5
  • C π‘₯ = βˆ’ 3 , 𝑦 = βˆ’ 5
  • D π‘₯ = 1 , 𝑦 = βˆ’ 5

Q4:

Find the real values of π‘₯ and 𝑦 that satisfy the equation ( βˆ’ π‘₯ + 5 ) + 3 𝑦 𝑖 = 7 + 3 𝑖 .

  • A π‘₯ = 2 , 𝑦 = 3
  • B π‘₯ = βˆ’ 2 , 𝑦 = βˆ’ 1
  • C π‘₯ = 7 , 𝑦 = 3
  • D π‘₯ = βˆ’ 2 , 𝑦 = 1

Q5:

Find the real values of π‘₯ and 𝑦 that satisfy the equation ( 4 π‘₯ + 2 ) βˆ’ 𝑦 𝑖 = 1 0 + 7 𝑖 .

  • A π‘₯ = 8 , 𝑦 = 7
  • B π‘₯ = 2 , 𝑦 = 7
  • C π‘₯ = 1 0 , 𝑦 = 7
  • D π‘₯ = 2 , 𝑦 = βˆ’ 7

Q6:

What is βˆ’ 9 + ( 7 + 4 𝑖 ) + ( βˆ’ 4 βˆ’ 4 𝑖 ) βˆ’ ( 1 + 3 𝑖 ) ?

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

Q7:

What is 2 βˆ’ ( βˆ’ 1 βˆ’ 8 𝑖 ) βˆ’ ( 3 + 𝑖 ) βˆ’ ( βˆ’ 1 βˆ’ 2 𝑖 ) ?

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

Q8:

If the complex numbers 4 + 5 𝑖 and π‘Ž + 5 𝑖 are equal, what is the value of π‘Ž ?

Q9:

Find the real values of π‘₯ and 𝑦 that satisfy the equation 2 π‘₯ + 2 π‘₯ 𝑖 + 4 𝑦 βˆ’ 4 𝑦 𝑖 = 8 .

  • A π‘₯ = 8 , 𝑦 = 0
  • B π‘₯ = βˆ’ 2 , 𝑦 = βˆ’ 1
  • C π‘₯ = 2 , 𝑦 = βˆ’ 1
  • D π‘₯ = 2 , 𝑦 = 1

Q10:

Simplify ( 7 + 𝑖 ) βˆ’ ( 8 βˆ’ 9 𝑖 ) .

  • A βˆ’ 1 βˆ’ 1 0 𝑖
  • B 5 6 + 9 𝑖
  • C 5 6 βˆ’ 9 𝑖
  • D βˆ’ 1 + 1 0 𝑖
  • E 1 βˆ’ 1 0 𝑖

Q11:

Simplify ( βˆ’ 3 + 4 𝑖 ) βˆ’ ( 4 + 5 𝑖 ) .

  • A βˆ’ 7 + 𝑖
  • B βˆ’ 1 2 βˆ’ 2 0 𝑖
  • C βˆ’ 1 2 + 2 0 𝑖
  • D βˆ’ 7 βˆ’ 𝑖
  • E 7 + 𝑖

Q12:

Simplify ( 4 + 𝑖 ) βˆ’ ( 6 + 4 𝑖 ) .

  • A βˆ’ 2 + 3 𝑖
  • B 2 4 βˆ’ 4 𝑖
  • C 2 4 + 4 𝑖
  • D βˆ’ 2 βˆ’ 3 𝑖
  • E 2 + 3 𝑖

Q13:

Evaluate ( βˆ’ 4 βˆ’ 5 𝑖 ) βˆ’ ( 2 βˆ’ 6 𝑖 ) .

  • A βˆ’ 2 βˆ’ 1 1 𝑖
  • B 6 βˆ’ 𝑖
  • C 2 + 1 1 𝑖
  • D βˆ’ 6 + 𝑖
  • E βˆ’ 6 βˆ’ 1 1 𝑖

Q14:

Find the real values of π‘₯ and 𝑦 that satisfy the equation π‘₯ + 𝑦 𝑖 = 1 0 βˆ’ 7 𝑖 .

  • A π‘₯ = βˆ’ 1 0 , 𝑦 = 7
  • B π‘₯ = βˆ’ 1 0 , 𝑦 = βˆ’ 7
  • C π‘₯ = 1 0 , 𝑦 = 7
  • D π‘₯ = 1 0 , 𝑦 = βˆ’ 7
  • E π‘₯ = βˆ’ 7 , 𝑦 = 1 0

Q15:

Find the real values of π‘₯ and 𝑦 that satisfy the equation π‘₯ + 𝑦 𝑖 = 2 0 + 3 𝑖 .

  • A π‘₯ = βˆ’ 2 0 , 𝑦 = βˆ’ 3
  • B π‘₯ = βˆ’ 2 0 , 𝑦 = 3
  • C π‘₯ = 2 0 , 𝑦 = βˆ’ 3
  • D π‘₯ = 2 0 , 𝑦 = 3
  • E π‘₯ = 3 , 𝑦 = 2 0

Q16:

Simplify ( 7 + 3 𝑖 ) + ( 3 βˆ’ 2 𝑖 ) .

  • A 1 0 βˆ’ 𝑖
  • B 2 1 βˆ’ 6 𝑖
  • C 2 1 + 6 𝑖
  • D 1 0 + 𝑖

Q17:

Simplify ( βˆ’ 7 βˆ’ 4 𝑖 ) + ( 6 + 𝑖 ) .

  • A βˆ’ 1 + 3 𝑖
  • B βˆ’ 4 2 βˆ’ 4 𝑖
  • C βˆ’ 4 2 + 4 𝑖
  • D βˆ’ 1 βˆ’ 3 𝑖

Q18:

Simplify ( 6 βˆ’ 𝑖 ) + ( 4 βˆ’ 9 𝑖 ) .

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

Q19:

If π‘Ÿ = 1 0 + 6 𝑖 and 𝑠 = 4 βˆ’ 3 𝑖 , find π‘Ÿ βˆ’ 𝑠 .

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

Q20:

Given that 𝑍 = βˆ’ 9 βˆ’ 9 √ 3 𝑖 1 and 𝑍 = 4 + 4 √ 3 𝑖 2 , determine the principal argument of ( 𝑍 βˆ’ 𝑍 ) 2 1 .

  • A 1 8 0 ∘
  • B 2 4 0 ∘
  • C 3 0 0 ∘
  • D 6 0 ∘

Q21:

If the complex numbers 7 + π‘Ž 𝑖 and 𝑏 βˆ’ 3 𝑖 are equal, what are the values of π‘Ž and 𝑏 ?

  • A π‘Ž = βˆ’ 7 , 𝑏 = 3
  • B π‘Ž = 7 , 𝑏 = βˆ’ 3
  • C π‘Ž = 3 , 𝑏 = βˆ’ 7
  • D π‘Ž = βˆ’ 3 , 𝑏 = 7
  • E π‘Ž = βˆ’ 3 , 𝑏 = βˆ’ 7

Q22:

Find the real values of π‘₯ and 𝑦 that satisfy the equation 4 π‘₯ + 2 𝑦 + ( π‘₯ βˆ’ 𝑦 ) 𝑖 = 8 + 8 𝑖 .

  • A π‘₯ = 8 , 𝑦 = 8
  • B π‘₯ = βˆ’ 4 , 𝑦 = 4
  • C π‘₯ = 4 , 𝑦 = 4
  • D π‘₯ = 4 , 𝑦 = βˆ’ 4

Q23:

Determine the real values of π‘₯ and 𝑦 that satisfy the equation π‘₯ + 𝑦 𝑖 = ( βˆ’ 1 9 + 7 𝑖 ) + ( 1 βˆ’ 4 𝑖 ) .

  • A π‘₯ = 3 , 𝑦 = βˆ’ 1 8
  • B π‘₯ = βˆ’ 2 0 , 𝑦 = 1 1
  • C π‘₯ = βˆ’ 1 9 , 𝑦 = βˆ’ 2 8
  • D π‘₯ = βˆ’ 1 8 , 𝑦 = 3

Q24:

If π‘Ÿ = 5 + 2 𝑖 and 𝑠 = 9 βˆ’ 𝑖 , find R e ( π‘Ÿ βˆ’ 𝑠 ) .

  • A14
  • B3
  • C1
  • D βˆ’ 4
  • E47

Q25:

Determine the real values of π‘₯ and 𝑦 that satisfy the equation 5 π‘₯ + 2 + ( 3 𝑦 βˆ’ 5 ) 𝑖 = βˆ’ 3 + 4 𝑖 .

  • A π‘₯ = 1 , 𝑦 = 3
  • B π‘₯ = 1 , 𝑦 = βˆ’ 3
  • C π‘₯ = βˆ’ 1 , 𝑦 = βˆ’ 3
  • D π‘₯ = βˆ’ 1 , 𝑦 = 3

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