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Worksheet: Complex Number Conjugates

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

Q1:

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

  • A 7 βˆ’ 𝑖 , βˆ’ 2 𝑖
  • B 7 + 𝑖 , 0
  • C βˆ’ 7 + 𝑖 , 1 4 𝑖
  • D βˆ’ 7 + 𝑖 , βˆ’ 1 4

Q2:

What is the conjugate of the complex number 4 + 3 𝑖 ?

  • A βˆ’ 4 βˆ’ 3 𝑖
  • B βˆ’ 4 + 3 𝑖
  • C 3 + 4 𝑖
  • D 4 βˆ’ 3 𝑖
  • E 3 βˆ’ 4 𝑖

Q3:

Is 8 𝑖 + 1 0 the complex conjugate of the number βˆ’ 8 𝑖 + 1 0 ?

  • Ayes
  • Bno

Q4:

Is it true that | 𝑧 | = | 𝑧 | βˆ— for all 𝑧 ?

  • Ayes
  • Bno

Q5:

Put 1 + 2 𝑖 9 + 7 𝑖 in the form π‘₯ + 𝑦 𝑖 .

  • A 2 3 3 2 + 1 1 3 2 𝑖
  • B βˆ’ 2 3 1 3 0 βˆ’ 1 1 1 3 0 𝑖
  • C βˆ’ 2 3 3 2 βˆ’ 1 1 3 2 𝑖
  • D 2 3 1 3 0 + 1 1 1 3 0 𝑖

Q6:

Put βˆ’ 1 2 𝑖 ( βˆ’ 1 + 𝑖 ) 2 in the form π‘₯ + 𝑦 𝑖 .

Q7:

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

  • A βˆ’ 1 βˆ’ 𝑖 , 0
  • B 1 βˆ’ 𝑖 , 0
  • C 1 βˆ’ 𝑖 , 1
  • D 1 βˆ’ 𝑖 , 2

Q8:

Given that π‘₯ = ( 2 βˆ’ 𝑖 ) and 𝑦 = ( 2 + 𝑖 ) , determine the value of π‘₯ βˆ’ π‘₯ 𝑦 + 𝑦 2 2 .

Q9:

Simplify 2 βˆ’ 2 𝑖 3 βˆ’ 𝑖 .

  • A 2 βˆ’ 4 𝑖 5
  • B 2 βˆ’ 2 𝑖 5
  • C 2 3 βˆ’ 2 𝑖
  • D 4 βˆ’ 2 𝑖 5
  • E 1 2 + 4 𝑖 5

Q10:

Express 1 ( βˆ’ 3 + 𝑖 ) 2 in the form π‘Ž + 𝑏 𝑖 .

  • A 4 5 + 3 5 𝑖
  • B 2 2 5 βˆ’ 3 5 0 𝑖
  • C 4 5 βˆ’ 3 5 𝑖
  • D 2 2 5 + 3 5 0 𝑖
  • E βˆ’ 2 2 5 + 3 5 0 𝑖

Q11:

Solve 2 𝑧 βˆ’ 𝑧 = 5 in β„‚ .

Q12:

If 𝑠 = 8 + 2 𝑖 , what is 𝑠 + 𝑠 βˆ— ?

Q13:

Given that | 𝑍 | + | 𝑍 | = 1 2 , determine the value of | 𝑍 𝑖 | .

Q14:

If 𝑧 = βˆ’ 8 𝑖 ,what is 𝑧 βˆ— ?

  • A8
  • B βˆ’ 8 𝑖
  • C βˆ’ 8
  • D 8 𝑖
  • E βˆ’ 𝑖 8

Q15:

Is it true that 𝑧 βˆ’ 𝑧 = 2 𝑖 ( 𝑧 ) βˆ— I m for all 𝑧 ?

  • Ayes
  • Bno

Q16:

Is βˆ’ 9 the complex conjugate of the number βˆ’ 9 ?

  • Ayes
  • Bno

Q17:

Is 5 the complex conjugate of the number 5?

  • Ayes
  • Bno

Q18:

Given that | 𝑍 | = 3 , determine the value of 𝑍 𝑍 .

Q19:

Is the sum of a number and its complex conjugate always a real number?

  • Ayes
  • Bno

Q20:

Is the product of a number and its complex conjugate always a real number?

  • Ayes
  • Bno

Q21:

If πœƒ is the principal argument of the complex number 𝑍 then what is the principal argument of 𝑍 ?

  • A πœ‹ βˆ’ πœƒ
  • B πœƒ
  • C βˆ’ πœ‹ + πœƒ
  • D βˆ’ πœƒ

Q22:

Put βˆ’ 9 + 𝑖 + 3 𝑖 βˆ’ 5 𝑖 5 βˆ’ 𝑖 + 5 𝑖 + 2 𝑖 2 3 2 3 in the form π‘Ž + 𝑏 𝑖 .

  • A βˆ’ 2 + 4 𝑖
  • B βˆ’ 4 + 1 2 𝑖
  • C βˆ’ 4 βˆ’ 1 2 𝑖
  • D βˆ’ 2 βˆ’ 4 𝑖

Q23:

Is it true that 𝑧 + 𝑧 = 2 ( 𝑧 ) βˆ— R e for all 𝑧 ?

  • Ayes
  • Bno

Q24:

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

  • A 𝑧 𝑖
  • B βˆ’ 𝑧
  • C βˆ’ 𝑧 𝑖
  • D 𝑧

Q25:

How do you find the conjugate of a complex number?

  • AChange the sign of both the real and imaginary parts.
  • BChange the sign of its real part.
  • CSwap the real and imaginary parts.
  • DChange the sign of its imaginary part.
  • ESwap the real and imaginary parts, then change the sign of them both.

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