Worksheet: Multiplying Complex Numbers

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

Q1:

Expand and simplify (4−𝑖)(3+2𝑖).

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

Q2:

Multiply (−3+𝑖) by (2+5𝑖).

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

Q3:

What is −7𝑖(−5+5𝑖)?

  • 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+5𝑖)(3−𝑖)?

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

Q5:

Simplify (7+6𝑖)(2−9𝑖).

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

Q6:

If 𝑟=2+7𝑖 and 𝑠=1+2𝑖, what is 𝑟×𝑠?

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

Q7:

Simplify (3−6𝑖)(2−𝑖).

  • A − 1 5 𝑖
  • B − 2 5 − 3 7 𝑖
  • C 8 − 1 1 𝑖
  • D − 9 0 − 4 5 𝑖
  • E − 2 7 − 3 6 𝑖

Q8:

If 𝑟=2+𝑖, express 𝑟 in the form 𝑎+𝑏𝑖.

  • A 6 + 7 𝑖
  • B 2 + 1 1 𝑖
  • C 8 + 𝑖
  • D 1 1 − 2 𝑖
  • E 8 − 𝑖

Q9:

Given that 𝑍=5√3−5𝑖, determine the algebraic form of 𝑍.

  • A − 5 0 + 5 0 √ 3 𝑖
  • B − 5 0 − 5 0 √ 3 𝑖
  • C 5 0 − 5 0 √ 3 𝑖
  • D 5 0 + 5 0 √ 3 𝑖

Q10:

Simplify 5−𝑖5−𝑖5−𝑖.

  • A − 1 3 0 − 2 6 𝑖
  • B 1 0 6 − 1 6 𝑖
  • C 1 3 0 − 2 6 𝑖
  • D − 1 3 0 + 2 6 𝑖

Q11:

Simplify √17−√−11√11−√−17.

  • A − 2 8 𝑖
  • B 1 6 8 − 3 7 4 𝑖
  • C 2 8 𝑖
  • D 1 6 8 + 3 7 4 𝑖

Q12:

Calculate 8+√−288−√−28.

Q13:

Simplify (11−8𝑖)(11+8𝑖)+(13−6𝑖)(13+6𝑖).

Q14:

What is (−5−𝑖)?

  • A − 2 4 − 1 0 𝑖
  • B − 1 0 − 2 𝑖
  • C26
  • D 2 4 + 1 0 𝑖

Q15:

What is −9−2𝑖−7−7𝑖+9𝑖?

  • A − 1 4 + 4 9 𝑖
  • B − 2 7 0 𝑖
  • C − 1 4 − 7 𝑖
  • D − 5 − 7 𝑖
  • E 4 2 + 4 9 𝑖

Q16:

Simplify 6−5𝑖.

  • A 1 1 − 6 0 𝑖
  • B 1 1 + 6 0 𝑖
  • C − 2 3 4 + 4 1 5 𝑖
  • D − 2 3 4 − 4 1 5 𝑖
  • E 4 1 5 + 2 3 4 𝑖

Q17:

Compute the product of 2+3𝑖 and 4+6𝑖.

  • A 6 + 9 𝑖
  • B − 1 0 + 2 4 𝑖
  • C 2 + 3 𝑖
  • D2

Q18:

If 𝑟=−2+4𝑖 and 𝑠=8−𝑖, find (𝑟−𝑠).

  • A 7 5 − 1 0 0 𝑖
  • B 1 0 0 + 2 5 𝑖
  • C 1 2 5 − 1 0 0 𝑖
  • D − 7 5
  • E 1 0 0 − 7 5 𝑖

Q19:

What is (2−7𝑖)+(−4−3𝑖)?

  • A − 4 1 − 2 5 𝑖
  • B − 4 5 − 2 8 𝑖
  • C − 4 1 − 3 1 𝑖
  • D − 4 9 − 3 1 𝑖
  • E − 2 − 1 0 𝑖

Q20:

Determine all the real values of 𝑥 and 𝑦 that satisfy the equation 86𝑖=(𝑥−22𝑖)(𝑦−𝑖)−38.

  • A 𝑥 = 1 0 1 1 , 𝑦 = − 6 6 5 or 𝑥=3,𝑦=−4
  • B 𝑥 = − 6 6 , 𝑦 = − 6 6 5 or 𝑥=−20,𝑦=−4
  • C 𝑥 = − 6 6 , 𝑦 = − 1 0 1 1 or 𝑥=−20,𝑦=−3
  • D 𝑥 = 1 0 1 1 , 𝑦 = 6 6 5 or 𝑥=3,𝑦=4

Q21:

If 𝑟=4−5𝑖, find 𝑟.

  • A 1 6 − 6 5 𝑖
  • B − 9 − 4 0 𝑖
  • C 4 1 − 4 0 𝑖
  • D 1 6 + 2 5 𝑖
  • E 1 6 − 1 5 𝑖

Q22:

If 𝑧=−1√2−𝑖 and 𝑧=−12+√2𝑖, is it true that 𝑧=𝑧?

  • Ano
  • Byes

Q23:

Given that (𝑥+𝑦𝑖)(2−𝑖)+(5𝑥−2𝑦𝑖)(2+𝑖)=−18, where 𝑥 and 𝑦 are real numbers, find the value of 𝑥 and the value of 𝑦.

  • A 𝑥 = − 1 , 𝑦 = − 2
  • B 𝑥 = − 1 , 𝑦 = 2
  • C 𝑥 = − 1 , 𝑦 = − 4
  • D 𝑥 = 1 , 𝑦 = 0

Q24:

Given that 𝑥+𝑦𝑖=(2−𝑖), where 𝑥 and 𝑦 are real numbers, find the value of 𝑥 and the value of 𝑦.

  • A 𝑥 = 2 , 𝑦 = − 1
  • B 𝑥 = 3 , 𝑦 = − 4
  • C 𝑥 = 2 , 𝑦 = − 1 1
  • D 𝑥 = 2 , 𝑦 = 1 1
  • E 𝑥 = 3 , 𝑦 = 4

Q25:

Given that 3𝑥−4𝑦𝑖=(4+𝑖), where 𝑥 and 𝑦 are real numbers, find the value of 𝑥 and the value of 𝑦.

  • A 𝑥 = 1 6 , 𝑦 = 1
  • B 𝑥 = 5 , 𝑦 = 2
  • C 𝑥 = 5 , 𝑦 = − 2
  • D 𝑥 = 4 , 𝑦 = 1
  • E 𝑥 = 4 , 𝑦 = − 1

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