Lesson Worksheet: Complex Number Conjugates Mathematics • 12th Grade

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 27𝑖?

  • A7+2𝑖
  • B7+2𝑖
  • C27𝑖
  • D2+7𝑖
  • E2+7𝑖

Q3:

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

  • A𝑧𝑖
  • B𝑧
  • C𝑧
  • D𝑧𝑖

Q4:

If 𝑠=8+2𝑖, what is 𝑠+𝑠?

Q5:

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

  • A7+𝑖, 14𝑖
  • B7𝑖, 2𝑖
  • C7+𝑖, 0
  • D7+𝑖, 14

Q6:

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

  • A1𝑖, 1
  • B1𝑖, 0
  • C1𝑖, 2
  • D1𝑖, 0

Q7:

Solve 𝑧𝑧+𝑧𝑧=4+2𝑖.

  • A𝑧=3𝑖, 𝑧=3𝑖
  • B𝑧=1+𝑖3, 𝑧=1𝑖3
  • C𝑧=3+𝑖, 𝑧=3𝑖
  • D𝑧=1+𝑖3, 𝑧=1+𝑖3
  • E𝑧=3+𝑖, 𝑧=3+𝑖

Q8:

Simplify (1𝑖)(1+𝑖)(1𝑖)+(1+𝑖).

Q9:

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

  • A𝑧=5232𝑖
  • B𝑧=53𝑖
  • C𝑧=3252𝑖
  • D𝑧=3+5𝑖
  • E𝑧=32+52𝑖

Q10:

Consider 𝑧=5𝑖3 and 𝑤=2+𝑖5.

Calculate 𝑧 and 𝑤.

  • A𝑧=5+𝑖3, 𝑤=2𝑖5
  • B𝑧=5+𝑖3, 𝑤=2𝑖5
  • C𝑧=5𝑖3, 𝑤=2+𝑖5
  • D𝑧=5𝑖3, 𝑤=2+𝑖5
  • E𝑧=35𝑖, 𝑤=5+𝑖2

Find 𝑧+𝑤 and (𝑧+𝑤).

  • A𝑧+𝑤=5+2+35𝑖, (𝑧+𝑤)=5+2+35𝑖
  • B𝑧+𝑤=5+2+35𝑖, (𝑧+𝑤)=5+235𝑖
  • C𝑧+𝑤=5+2+3+5𝑖, (𝑧+𝑤)=5+23+5𝑖
  • D𝑧+𝑤=5+235𝑖, (𝑧+𝑤)=5+235𝑖
  • E𝑧+𝑤=35+5+2𝑖, (𝑧+𝑤)=35+5+2𝑖

Find 𝑧𝑤 and (𝑧𝑤).

  • A𝑧𝑤=52+215+556𝑖, (𝑧𝑤)=52+21555+6𝑖
  • B𝑧𝑤=52+15556𝑖, (𝑧𝑤)=52+15556𝑖
  • C𝑧𝑤=52+21555+6𝑖, (𝑧𝑤)=52+215+55+6𝑖
  • D𝑧𝑤=55652+215𝑖, (𝑧𝑤)=556+52+215𝑖
  • E𝑧𝑤=52+15+556𝑖, (𝑧𝑤)=52+15+556𝑖

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