Worksheet: Multiplication of Complex Numbers

Practice

In this worksheet, we will practice multiplying two complex numbers.

Q1:

Expand and simplify ( 4 − 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 − 2 𝑖

Q2:

Multiply ( − 3 + 𝑖 ) by ( 2 + 5 𝑖 ) .

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

Q3:

What is − 7 𝑖 ( − 5 + 5 𝑖 ) ?

  • A − 3 5 + 3 5 𝑖
  • B − 3 5 − 3 5 𝑖
  • C 3 5 − 3 5 𝑖
  • D 3 5 + 3 5 𝑖

Q4:

What is ( − 9 + 5 𝑖 ) ( 3 − 𝑖 ) ?

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

Q5:

Simplify ( 7 + 6 𝑖 ) ( 2 − 9 𝑖 ) .

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

Q6:

Put 4 √ 3 + √ − 3 2 √ 3 − √ − 8 in the form 𝑎 + 𝑏 𝑖 .

  • A − 4 1 1 + 1 2 1 1 𝑖
  • B − 4 1 1 − 1 2 √ 6 1 1 𝑖
  • C − 4 1 1 − 1 2 1 1 𝑖
  • D − 4 1 1 + 1 2 √ 6 1 1 𝑖
  • E − 4 1 1 + 1 2 √ 6 𝑖

Q7:

Given that 𝑥 = 1 0 6 + 3 𝑖 and 𝑦 = − 2 − 6 𝑖 − 3 − 3 𝑖 , is 𝑥 the complex conjugate of 𝑦 ?

  • Ayes
  • Bno

Q8:

By what complex number would you multiply the numerator and denominator of the quotient 5 + 6 𝑖 3 − 2 𝑖 in order to simplify it?

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

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