Lesson Worksheet: Complex Number Conjugates Mathematics • 12th Grade

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


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.


What is the conjugate of the complex number 2βˆ’7𝑖?

  • A7+2𝑖
  • Bβˆ’7+2𝑖
  • Cβˆ’2βˆ’7𝑖
  • Dβˆ’2+7𝑖
  • E2+7𝑖


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

  • Aβˆ’π‘§π‘–
  • Bβˆ’π‘§
  • C𝑧
  • D𝑧𝑖


If 𝑠=8+2𝑖, what is 𝑠+𝑠?


Find the complex conjugate of βˆ’7βˆ’π‘– and the sum of this number with its complex conjugate.

  • Aβˆ’7+𝑖, 14𝑖
  • B7βˆ’π‘–, βˆ’2𝑖
  • C7+𝑖, 0
  • Dβˆ’7+𝑖, βˆ’14


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

  • A1βˆ’π‘–, 1
  • Bβˆ’1βˆ’π‘–, 0
  • C1βˆ’π‘–, 2
  • D1βˆ’π‘–, 0


Solve 𝑧𝑧+π‘§βˆ’π‘§=4+2𝑖.

  • A𝑧=√3βˆ’π‘–, 𝑧=βˆ’βˆš3βˆ’π‘–
  • B𝑧=1+π‘–βˆš3, 𝑧=1βˆ’π‘–βˆš3
  • C𝑧=βˆ’βˆš3+𝑖, 𝑧=√3βˆ’π‘–
  • D𝑧=1+π‘–βˆš3, 𝑧=βˆ’1+π‘–βˆš3
  • E𝑧=√3+𝑖, 𝑧=βˆ’βˆš3+𝑖


Simplify (1βˆ’π‘–)βˆ’(1+𝑖)(1βˆ’π‘–)+(1+𝑖).


Find the complex number 𝑧 that satisfies the equations 𝑧+𝑧=βˆ’5,π‘§βˆ’π‘§=3𝑖.

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


Consider 𝑧=5βˆ’π‘–βˆš3 and 𝑀=√2+π‘–βˆš5.

Calculate 𝑧 and 𝑀.

  • A𝑧=βˆ’5+π‘–βˆš3, 𝑀=βˆ’βˆš2βˆ’π‘–βˆš5
  • B𝑧=5+π‘–βˆš3, 𝑀=√2βˆ’π‘–βˆš5
  • C𝑧=5βˆ’π‘–βˆš3, 𝑀=√2+π‘–βˆš5
  • D𝑧=βˆ’5βˆ’π‘–βˆš3, 𝑀=βˆ’βˆš2+π‘–βˆš5
  • E𝑧=√3βˆ’5𝑖, 𝑀=√5+π‘–βˆš2

Find 𝑧+𝑀 and (𝑧+𝑀).

  • A𝑧+𝑀=5+√2+ο€»βˆš3βˆ’βˆš5𝑖, (𝑧+𝑀)=5+√2+ο€»βˆš3βˆ’βˆš5𝑖
  • B𝑧+𝑀=5+√2+ο€»βˆš3βˆ’βˆš5𝑖, (𝑧+𝑀)=5+√2βˆ’ο€»βˆš3βˆ’βˆš5𝑖
  • C𝑧+𝑀=5+√2+ο€»βˆš3+√5𝑖, (𝑧+𝑀)=5+√2βˆ’ο€»βˆš3+√5𝑖
  • D𝑧+𝑀=5+√2βˆ’ο€»βˆš3βˆ’βˆš5𝑖, (𝑧+𝑀)=5+√2βˆ’ο€»βˆš3βˆ’βˆš5𝑖
  • E𝑧+𝑀=√3βˆ’βˆš5+ο€»5+√2𝑖, (𝑧+𝑀)=√3βˆ’βˆš5+ο€»5+√2𝑖

Find 𝑧𝑀 and (𝑧𝑀).

  • A𝑧𝑀=5√2+2√15+ο€»5√5βˆ’βˆš6𝑖, (𝑧𝑀)=5√2+2√15βˆ’ο€»5√5+√6𝑖
  • B𝑧𝑀=5√2+√15βˆ’ο€»5√5βˆ’βˆš6𝑖, (𝑧𝑀)=5√2+√15βˆ’ο€»5√5βˆ’βˆš6𝑖
  • C𝑧𝑀=5√2+2√15βˆ’ο€»5√5+√6𝑖, (𝑧𝑀)=5√2+2√15+ο€»5√5+√6𝑖
  • D𝑧𝑀=5√5βˆ’βˆš6βˆ’ο€»5√2+2√15𝑖, (𝑧𝑀)=5√5βˆ’βˆš6+ο€»5√2+2√15𝑖
  • E𝑧𝑀=5√2+√15+ο€»5√5βˆ’βˆš6𝑖, (𝑧𝑀)=5√2+√15+ο€»5√5βˆ’βˆš6𝑖

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