Worksheet: Multiplying Complex Numbers

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

Q1:

Expand and simplify (4−𝑖)(3+2𝑖).

  • A14+5𝑖
  • B12+3𝑖
  • C12−2𝑖
  • D12+7𝑖
  • E10+5𝑖

Q2:

Multiply (−3+𝑖) by (2+5𝑖).

  • A−6+5𝑖
  • B−6−18𝑖
  • C−1−13𝑖
  • D−6−8𝑖
  • E−11−13𝑖

Q3:

What is −7𝑖(−5+5𝑖)?

  • A35−35𝑖
  • B−35−35𝑖
  • C−35+35𝑖
  • D35+35𝑖

Q4:

What is (−9+5𝑖)(3−𝑖)?

  • A−22+24𝑖
  • B−32+24𝑖
  • C−22−24𝑖
  • D5𝑖+24𝑖−27
  • E−27−5𝑖

Q5:

Simplify (7+6𝑖)(2−9𝑖).

  • A−40−51𝑖
  • B−40+75𝑖
  • C68+51𝑖
  • D68−51𝑖
  • E68+75𝑖

Q6:

If 𝑟=2+7𝑖 and 𝑠=1+2𝑖, what is 𝑟×𝑠?

  • A2+25𝑖
  • B2+14𝑖
  • C−12+11𝑖
  • D16+11𝑖
  • E2−3𝑖

Q7:

Simplify (3−6𝑖)(2−𝑖).

  • A−15𝑖
  • B−25−37𝑖
  • C8−11𝑖
  • D−90−45𝑖
  • E−27−36𝑖

Q8:

If 𝑟=2+𝑖, express 𝑟 in the form 𝑎+𝑏𝑖.

  • A6+7𝑖
  • B2+11𝑖
  • C8+𝑖
  • D11−2𝑖
  • E8−𝑖

Q9:

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

  • A−50+50√3𝑖
  • B−50−50√3𝑖
  • C50−50√3𝑖
  • D50+50√3𝑖

Q10:

Simplify 5−𝑖5−𝑖5−𝑖.

  • A−130−26𝑖
  • B106−16𝑖
  • C130−26𝑖
  • D−130+26𝑖

Q11:

Simplify √17−√−11√11−√−17.

  • A−28𝑖
  • B168−374𝑖
  • C28𝑖
  • D168+374𝑖

Q12:

Calculate 8+√−288−√−28.

Q13:

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

Q14:

What is (−5−𝑖)?

  • A−24−10𝑖
  • B−10−2𝑖
  • C26
  • D24+10𝑖

Q15:

What is −9−2𝑖−7−7𝑖+9𝑖?

  • A−14+49𝑖
  • B−270𝑖
  • C−14−7𝑖
  • D−5−7𝑖
  • E42+49𝑖

Q16:

Simplify 6−5𝑖.

  • A11−60𝑖
  • B11+60𝑖
  • C−234+415𝑖
  • D−234−415𝑖
  • E415+234𝑖

Q17:

Compute the product of 2+3𝑖 and 4+6𝑖.

  • A6+9𝑖
  • B−10+24𝑖
  • C2+3𝑖
  • D2

Q18:

If 𝑟=−2+4𝑖 and 𝑠=8−𝑖, find (𝑟−𝑠).

  • A75−100𝑖
  • B100+25𝑖
  • C125−100𝑖
  • D−75
  • E100−75𝑖

Q19:

What is (2−7𝑖)+(−4−3𝑖)?

  • A−41−25𝑖
  • B−45−28𝑖
  • C−41−31𝑖
  • D−49−31𝑖
  • E−2−10𝑖

Q20:

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

  • A𝑥=1011,𝑦=−665 or 𝑥=3,𝑦=−4
  • B𝑥=−66,𝑦=−665 or 𝑥=−20,𝑦=−4
  • C𝑥=−66,𝑦=−1011 or 𝑥=−20,𝑦=−3
  • D𝑥=1011,𝑦=665 or 𝑥=3,𝑦=4

Q21:

If 𝑟=4−5𝑖, find 𝑟.

  • A16−65𝑖
  • B−9−40𝑖
  • C41−40𝑖
  • D16+25𝑖
  • E16−15𝑖

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.

  • A𝑥=−1, 𝑦=−2
  • B𝑥=−1, 𝑦=2
  • C𝑥=−1, 𝑦=−4
  • D𝑥=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.

  • A𝑥=2, 𝑦=−1
  • B𝑥=3, 𝑦=−4
  • C𝑥=2, 𝑦=−11
  • D𝑥=2, 𝑦=11
  • E𝑥=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.

  • A𝑥=16, 𝑦=1
  • B𝑥=5, 𝑦=2
  • C𝑥=5, 𝑦=−2
  • D𝑥=4, 𝑦=1
  • E𝑥=4, 𝑦=−1

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