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Worksheet: Multiplying and Dividing Complex Numbers

In this worksheet, we will practice performing operations like multiplication and division on complex numbers.

Q1:

Expand and simplify ( 4 βˆ’ 𝑖 ) ( 3 + 2 𝑖 ) .

  • A 1 2 + 7 𝑖
  • B 1 0 + 5 𝑖
  • C 1 2 + 3 𝑖
  • D 1 4 + 5 𝑖
  • E 1 2 βˆ’ 2 𝑖

Q2:

Simplify 2 3 + 𝑖 .

  • A ( 3 βˆ’ 𝑖 ) 1 0
  • B 2 3 βˆ’ 2 𝑖
  • C 3 βˆ’ 𝑖
  • D ( 3 βˆ’ 𝑖 ) 5
  • E 2 3 + 2 𝑖

Q3:

Simplify 5 + 9 𝑖 4 + 7 𝑖 .

  • A βˆ’ 8 3 3 3 βˆ’ 1 3 3 𝑖
  • B 5 4 + 9 7 𝑖
  • C 9 1 3 + 2 8 6 5 𝑖
  • D 8 3 6 5 + 1 6 5 𝑖
  • E βˆ’ 1 5 1 1 βˆ’ 2 8 3 3 𝑖

Q4:

Simplify 4 βˆ’ 5 𝑖 7 + 3 𝑖 .

  • A 1 3 4 0 βˆ’ 4 7 4 0 𝑖
  • B 4 7 βˆ’ 5 3 𝑖
  • C βˆ’ 1 0 2 9 + 2 1 5 8 𝑖
  • D 1 3 5 8 βˆ’ 4 7 5 8 𝑖
  • E βˆ’ 1 2 + 2 1 4 0 𝑖

Q5:

Simplify 3 βˆ’ 6 𝑖 1 βˆ’ 5 𝑖 .

  • A βˆ’ 1 1 8 βˆ’ 3 8 𝑖
  • B 3 + 6 5 𝑖
  • C βˆ’ 9 1 3 βˆ’ 5 2 6 𝑖
  • D 3 3 2 6 + 9 2 6 𝑖
  • E 3 4 + 5 2 4 𝑖

Q6:

Simplify ( 7 + 6 𝑖 ) ( 2 βˆ’ 9 𝑖 ) .

  • A 6 8 + 7 5 𝑖
  • B βˆ’ 4 0 βˆ’ 5 1 𝑖
  • C βˆ’ 4 0 + 7 5 𝑖
  • D 6 8 βˆ’ 5 1 𝑖
  • E 6 8 + 5 1 𝑖

Q7:

Simplify 1 3 1 3 + 2 𝑖 .

  • A 1 6 9 1 6 5 βˆ’ 2 6 1 6 5 𝑖
  • B 1 6 9 1 7 3 + 2 6 1 7 3 𝑖
  • C 1 6 9 1 6 5 + 2 6 1 6 5 𝑖
  • D 1 6 9 1 7 3 βˆ’ 2 6 1 7 3 𝑖

Q8:

Simplify ( 8 + 7 𝑖 ) ( 1 + 8 𝑖 ) ( 6 + 4 𝑖 ) .

  • A βˆ’ 1 5 + 3 0 9 1 0 𝑖
  • B 1 1 3 βˆ’ 3 0 9 2 6 𝑖
  • C 1 5 βˆ’ 3 0 9 1 0 𝑖
  • D βˆ’ 1 1 3 + 3 0 9 2 6 𝑖

Q9:

Simplify βˆ’ 1 βˆ’ 9 𝑖 + 5 𝑖 βˆ’ 7 𝑖 βˆ’ 6 + 4 𝑖 βˆ’ 4 𝑖 + 2 𝑖 2 3 2 3 .

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

Q10:

What is ( βˆ’ 9 + 5 𝑖 ) ( 3 βˆ’ 𝑖 ) ?

  • A βˆ’ 2 2 βˆ’ 2 4 𝑖
  • B βˆ’ 3 2 + 2 4 𝑖
  • C 5 𝑖 + 2 4 𝑖 βˆ’ 2 7 2
  • D βˆ’ 2 2 + 2 4 𝑖
  • E βˆ’ 2 7 βˆ’ 5 𝑖

Q11:

What is ( βˆ’ 1 βˆ’ 3 𝑖 ) ( βˆ’ 9 βˆ’ 5 𝑖 ) ?

  • A βˆ’ 6 βˆ’ 3 2 𝑖
  • B 2 4 + 3 2 𝑖
  • C βˆ’ 1 5 𝑖 + 3 2 𝑖 + 9 2
  • D βˆ’ 6 + 3 2 𝑖
  • E 9 + 1 5 𝑖

Q12:

What is ( 4 + 2 𝑖 ) ( 6 + 2 𝑖 ) ?

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

Q13:

Simplify βˆ’ 7 + 𝑖 + 3 𝑖 βˆ’ 6 𝑖 βˆ’ 2 βˆ’ 𝑖 βˆ’ 𝑖 βˆ’ 𝑖 2 3 2 3 .

  • A 1 0 + 7 𝑖
  • B 4 βˆ’ 3 𝑖
  • C 4 + 3 𝑖
  • D 1 0 βˆ’ 7 𝑖

Q14:

Let 𝐿 = 2 2 βˆ’ 2 𝑖 and 𝑀 = 3 βˆ’ 6 𝑖 9 βˆ’ 3 𝑖 . Is 𝑀 the complex conjugate of 𝐿 ?

  • Ayes
  • Bno

Q15:

Simplify ( βˆ’ 3 + 2 𝑖 ) ( 3 + 3 𝑖 ) ( 4 + 𝑖 ) ( 4 + 4 𝑖 ) .

  • A βˆ’ 1 5 3 4 βˆ’ 3 3 6 8 𝑖
  • B 1 5 3 4 + 3 3 6 8 𝑖
  • C 1 5 3 4 βˆ’ 3 3 6 8 𝑖
  • D βˆ’ 1 5 3 4 + 3 3 6 8 𝑖

Q16:

Put 2 βˆ’ 5 + 5 𝑖 in the form π‘Ž + 𝑏 𝑖 .

  • A 0 . 2 + 0 . 2 𝑖
  • B βˆ’ 0 . 2 + 0 . 2 𝑖
  • C 0 . 2 βˆ’ 0 . 2 𝑖
  • D βˆ’ 0 . 2 βˆ’ 0 . 2 𝑖

Q17:

Simplify βˆ’ 1 2 βˆ’ 4 𝑖 2 𝑖 .

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

Q18:

Solve the equation 𝑖 𝑧 = βˆ’ 4 + 3 𝑖 .

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

Q19:

Simplify 4 + 𝑖 4 βˆ’ 𝑖 .

  • A 1 7 + 8 𝑖 1 5
  • B 1 5 + 8 𝑖 1 5
  • C 1 βˆ’ 𝑖
  • D 1 5 + 8 𝑖 1 7
  • E 1 7 1 5 + 8 𝑖

Q20:

What is βˆ’ 7 𝑖 ( βˆ’ 5 + 5 𝑖 ) ?

  • A βˆ’ 3 5 + 3 5 𝑖
  • B βˆ’ 3 5 βˆ’ 3 5 𝑖
  • C 3 5 βˆ’ 3 5 𝑖
  • D 3 5 + 3 5 𝑖

Q21:

What is βˆ’ 1 0 𝑖 ( βˆ’ 4 βˆ’ 6 𝑖 ) ?

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

Q22:

Put βˆ’ 1 8 βˆ’ 9 𝑖 3 𝑖 in the form π‘Ž + 𝑏 𝑖 .

  • A βˆ’ 9 + 1 8 𝑖
  • B 2 7 βˆ’ 5 4 𝑖
  • C 3 + 5 4 𝑖
  • D βˆ’ 3 + 6 𝑖

Q23:

If π‘Ž + 𝑏 𝑖 = βˆ’ 3 βˆ’ 5 𝑖 βˆ’ 3 + 5 𝑖 , is it true that π‘Ž + 𝑏 = 1 2 2 ?

  • Ayes
  • Bno

Q24:

Multiply ( βˆ’ 3 + 𝑖 ) by ( 2 + 5 𝑖 ) .

  • A βˆ’ 6 βˆ’ 1 8 𝑖
  • B βˆ’ 1 βˆ’ 1 3 𝑖
  • C βˆ’ 6 βˆ’ 8 𝑖
  • D βˆ’ 1 1 βˆ’ 1 3 𝑖
  • E βˆ’ 6 + 5 𝑖

Q25:

Express ( 5 + 5 𝑖 ) ( 8 βˆ’ 4 𝑖 ) 1 βˆ’ 𝑖 in the form π‘Ž + 𝑏 𝑖 .

  • A 4 0 βˆ’ 2 0 𝑖
  • B 6 0 + 2 0 𝑖
  • C 2 8 + 1 6 𝑖
  • D 2 0 + 4 0 𝑖
  • E βˆ’ 5 + 4 0 𝑖

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