Worksheet: Equating, Adding, and Subtracting Complex Numbers

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

Q1:

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

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

Q2:

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

Q3:

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

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

Q4:

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

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

Q5:

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

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

Q6:

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

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

Q7:

Simplify ( 6 3 𝑖 ) + ( 5 𝑖 ) .

  • A 1 1 + 4 𝑖
  • B 4 + 1 1 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 + 𝑦 𝑖 = 1 0 7 𝑖 .

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

Q9:

Simplify ( 7 + 3 𝑖 ) + ( 3 2 𝑖 ) .

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

Q10:

Simplify ( 7 + 𝑖 ) ( 8 9 𝑖 ) .

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

Q11:

Determine the real values of 𝑥 and 𝑦 that satisfy the equation 𝑥 + 𝑦 𝑖 = ( 1 9 + 7 𝑖 ) + ( 1 4 𝑖 ) .

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

Q12:

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

  • 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 4 𝑥 + 2 𝑦 + ( 𝑥 𝑦 ) 𝑖 = 8 + 8 𝑖 .

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

Q14:

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

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

Q15:

Evaluate ( 4 5 𝑖 ) ( 2 6 𝑖 ) .

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

Q16:

If 𝑟 = 1 0 + 6 𝑖 and 𝑠 = 4 3 𝑖 , find 𝑟 𝑠 .

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

Q17:

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

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

Q18:

If 𝑟 = 5 + 2 𝑖 and 𝑠 = 9 𝑖 , find R e ( 𝑟 𝑠 ) .

  • A14
  • B3
  • C1
  • D 4
  • E47

Q19:

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

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

Q20:

If 𝑟 = 2 + 3 𝑖 and 𝑠 = 4 5 𝑖 , find 𝑟 + 𝑠 .

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

Q21:

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

  • Ayes
  • Bno

Q22:

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

Q23:

Add 4 2 𝑖 to 3 + 7 𝑖 .

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

Q24:

If 𝑟 = 4 + 3 𝑖 and 𝑠 = 2 𝑖 , find 𝑟 + 𝑠 𝑖 .

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

Q25:

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

  • A 12
  • B 2
  • C 4
  • D 6
  • E 16

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