Lesson Worksheet: Complex Number Conjugates Mathematics • 12th Grade

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In this worksheet, we will practice using the properties of conjugate numbers to evaluate an expression.

Q1:

How do you find the conjugate of a complex number?

  • AChange the sign of both the real and imaginary parts.
  • BSwap the real and imaginary parts.
  • CChange the sign of its imaginary part.
  • DSwap the real and imaginary parts, then change the sign of them both.
  • EChange the sign of its real part.

Q2:

What is the conjugate of the complex number 2−7𝑖?

  • A7+2𝑖
  • B−7+2𝑖
  • C−2−7𝑖
  • D−2+7𝑖
  • E2+7𝑖

Q3:

If 𝑧 is a real number, what will its conjugate be equal to?

  • A−𝑧𝑖
  • B−𝑧
  • C𝑧
  • D𝑧𝑖

Q4:

If 𝑠=8+2𝑖, what is 𝑠+𝑠?

Q5:

Find the complex conjugate of −7−𝑖 and the sum of this number with its complex conjugate.

  • A−7+𝑖, 14𝑖
  • B7−𝑖, −2𝑖
  • C7+𝑖, 0
  • D−7+𝑖, −14

Q6:

Find the complex conjugate of 1+𝑖 and the product of this number with its complex conjugate.

  • A1−𝑖, 1
  • B−1−𝑖, 0
  • C1−𝑖, 2
  • D1−𝑖, 0

Q7:

Solve 𝑧𝑧+𝑧−𝑧=4+2𝑖.

  • A𝑧=√3−𝑖, 𝑧=−√3−𝑖
  • B𝑧=1+𝑖√3, 𝑧=1−𝑖√3
  • C𝑧=−√3+𝑖, 𝑧=√3−𝑖
  • D𝑧=1+𝑖√3, 𝑧=−1+𝑖√3
  • E𝑧=√3+𝑖, 𝑧=−√3+𝑖

Q8:

Simplify (1−𝑖)−(1+𝑖)(1−𝑖)+(1+𝑖).

Q9:

Find the complex number 𝑧 that satisfies the equations 𝑧+𝑧=−5,𝑧−𝑧=3𝑖.

  • A𝑧=−52−32𝑖
  • B𝑧=5−3𝑖
  • C𝑧=−32−52𝑖
  • D𝑧=3+5𝑖
  • E𝑧=−32+52𝑖

Q10:

Consider 𝑧=5−𝑖√3 and 𝑤=√2+𝑖√5.

Calculate 𝑧 and 𝑤.

  • A𝑧=−5+𝑖√3, 𝑤=−√2−𝑖√5
  • B𝑧=5+𝑖√3, 𝑤=√2−𝑖√5
  • C𝑧=5−𝑖√3, 𝑤=√2+𝑖√5
  • D𝑧=−5−𝑖√3, 𝑤=−√2+𝑖√5
  • E𝑧=√3−5𝑖, 𝑤=√5+𝑖√2

Find 𝑧+𝑤 and (𝑧+𝑤).

  • A𝑧+𝑤=5+√2+√3−√5𝑖, (𝑧+𝑤)=5+√2+√3−√5𝑖
  • B𝑧+𝑤=5+√2+√3−√5𝑖, (𝑧+𝑤)=5+√2−√3−√5𝑖
  • C𝑧+𝑤=5+√2+√3+√5𝑖, (𝑧+𝑤)=5+√2−√3+√5𝑖
  • D𝑧+𝑤=5+√2−√3−√5𝑖, (𝑧+𝑤)=5+√2−√3−√5𝑖
  • E𝑧+𝑤=√3−√5+5+√2𝑖, (𝑧+𝑤)=√3−√5+5+√2𝑖

Find 𝑧𝑤 and (𝑧𝑤).

  • A𝑧𝑤=5√2+2√15+5√5−√6𝑖, (𝑧𝑤)=5√2+2√15−5√5+√6𝑖
  • B𝑧𝑤=5√2+√15−5√5−√6𝑖, (𝑧𝑤)=5√2+√15−5√5−√6𝑖
  • C𝑧𝑤=5√2+2√15−5√5+√6𝑖, (𝑧𝑤)=5√2+2√15+5√5+√6𝑖
  • D𝑧𝑤=5√5−√6−5√2+2√15𝑖, (𝑧𝑤)=5√5−√6+5√2+2√15𝑖
  • E𝑧𝑤=5√2+√15+5√5−√6𝑖, (𝑧𝑤)=5√2+√15+5√5−√6𝑖

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