Lesson Worksheet: Multiplying Complex Numbers Mathematics • 12th Grade

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

Q1:

If 𝑟=−5+2𝑖 and 𝑠=−8−2𝑖, find 2𝑟+3𝑠.

  • A−34−2𝑖
  • B34+2𝑖
  • C−34+2𝑖
  • D14+10𝑖
  • E1+10𝑖

Q2:

What is −7𝑖(−5+5𝑖)?

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

Q3:

Multiply (−3+𝑖) by (2+5𝑖).

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

Q4:

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

Q5:

If 𝑟=−2+4𝑖 and 𝑠=8−𝑖, find (𝑟−𝑠).

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

Q6:

Find Re(7−2𝑖).

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:

Find the value of 𝑏 such that the complex number (3+4𝑖)(4+𝑏𝑖) is purely imaginary.

Q10:

Solve the equation 𝑖𝑧=−4+3𝑖.

  • A𝑧=−4+3𝑖
  • B𝑧=−3−4𝑖
  • C𝑧=3+4𝑖
  • D𝑧=−3+4𝑖
  • E𝑧=3−4𝑖

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