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Lesson: De Moivre's Theorem

Sample Question Videos

Worksheet • 8 Questions • 1 Video

Q1:

What is ( 1 βˆ’ 2 𝑖 ) 4 ?

  • A βˆ’ 7 + 2 4 𝑖
  • B 1 βˆ’ 2 𝑖
  • C βˆ’ 3 βˆ’ 4 𝑖
  • D 4 βˆ’ 8 𝑖
  • E 5 + 1 0 𝑖

Q2:

Use De Moivre’s theorem to find the two square roots of 9 ο€Ό 2 πœ‹ 3 + 𝑖 2 πœ‹ 3  c o s s i n .

  • A  3 2 + 3 √ 3 2 𝑖 , βˆ’ 3 2 βˆ’ 3 √ 3 2 𝑖 
  • B  βˆ’ 1 2 βˆ’ 1 2 𝑖 , 1 2 + 1 2 𝑖 
  • C  3 2 + 3 √ 3 2 𝑖 , βˆ’ 3 2 + 3 √ 3 2 𝑖 
  • D  √ 3 2 βˆ’ 1 2 𝑖 , βˆ’ √ 3 2 + 1 2 𝑖 
  • E { βˆ’ 3 , 3 }

Q3:

If 𝑍 = π‘Ÿ ( πœƒ + 𝑖 πœƒ ) c o s s i n , what is 𝑍 𝑛 ?

  • A π‘Ÿ ( 𝑛 πœƒ + 𝑖 𝑛 πœƒ ) 𝑛 c o s s i n
  • B π‘Ÿ ( πœƒ + 𝑖 πœƒ ) 𝑛 c o s s i n
  • C π‘Ÿ ο€½ πœƒ 𝑛 + 𝑖 πœƒ 𝑛  c o s s i n
  • D π‘Ÿ ( 𝑛 πœƒ + 𝑖 𝑛 πœƒ ) c o s s i n

Q4:

What is ( 1 + 𝑖 ) 1 0 ?

  • A 3 2 𝑖
  • B 1 + 𝑖
  • C 1 0 𝑖
  • D 2 + 2 𝑖
  • E2

Q5:

What is ( βˆ’ 1 βˆ’ 3 𝑖 ) 4 ?

  • A 2 8 βˆ’ 9 6 𝑖
  • B βˆ’ 1 βˆ’ 3 𝑖
  • C βˆ’ 8 + 6 𝑖
  • D βˆ’ 4 βˆ’ 1 2 𝑖
  • E βˆ’ 1 0 + 3 0 𝑖

Q6:

Use De Moivre’s theorem to find the two square roots of c o s s i n πœ‹ 3 + 𝑖 πœ‹ 3 .

  • A  √ 3 2 + 1 2 𝑖 , βˆ’ √ 3 2 βˆ’ 1 2 𝑖 
  • B  1 2 + √ 2 𝑖 , βˆ’ 1 2 βˆ’ √ 2 𝑖 
  • C  √ 3 2 + 1 2 𝑖 , 𝑖 
  • D  1 2 βˆ’ √ 3 2 𝑖 , βˆ’ 1 2 + √ 3 2 𝑖 
  • E { 𝑖 , βˆ’ 𝑖 }

Q7:

Use De Moivre’s theorem to find the two square roots of 9 ο€» πœ‹ 3 + 𝑖 πœ‹ 3  c o s s i n .

  • A  3 √ 3 2 + 3 2 𝑖 , βˆ’ 3 √ 3 2 βˆ’ 3 2 𝑖 
  • B  1 2 + √ 2 𝑖 , βˆ’ 1 2 βˆ’ √ 2 𝑖 
  • C  3 √ 3 2 + 3 2 𝑖 , 3 𝑖 
  • D { βˆ’ 1 , 1 }
  • E { 3 𝑖 , βˆ’ 3 𝑖 }

Q8:

What is ( βˆ’ 1 + 𝑖 ) 8 ?

  • A16
  • B βˆ’ 1 + 𝑖
  • C βˆ’ 8 𝑖
  • D βˆ’ 8 + 8 𝑖
  • E2
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