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Worksheet: Euler's Formula

Q1:

Find the numerical value of 𝑒 + 𝑒 1 1 πœ‹ 6 1 1 πœ‹ 6 𝑖 βˆ’ 𝑖 .

  • A βˆ’ √ 3
  • B0
  • C √ 3 2
  • D √ 3

Q2:

Find the numerical value of 𝑒 βˆ’ 𝑒 2 πœ‹ 𝑖 βˆ’ 2 πœ‹ 𝑖 .

  • A βˆ’ 2
  • B1
  • C2
  • D0

Q3:

Given that π‘Ž 𝑒 + 𝑏 𝑒 = ( 2 πœƒ ) βˆ’ 5 𝑖 ( 2 πœƒ ) 2 𝑖 πœƒ βˆ’ 2 𝑖 πœƒ c o s s i n , where π‘Ž ∈ ℝ and 𝑏 ∈ ℝ , find π‘Ž and 𝑏 .

  • A π‘Ž = βˆ’ 2 , 𝑏 = βˆ’ 1
  • B π‘Ž = 2 , 𝑏 = 3
  • C π‘Ž = 2 , 𝑏 = βˆ’ 1
  • D π‘Ž = βˆ’ 2 , 𝑏 = 3

Q4:

Given that π‘Ž 𝑒 + 𝑏 𝑒 = βˆ’ 6 ( 2 πœƒ ) βˆ’ 6 𝑖 ( 2 πœƒ ) 2 𝑖 πœƒ βˆ’ 2 𝑖 πœƒ c o s s i n , where π‘Ž ∈ ℝ and 𝑏 ∈ ℝ , find π‘Ž and 𝑏 .

  • A π‘Ž = βˆ’ 6 , 𝑏 = βˆ’ 1 2
  • B π‘Ž = 6 , 𝑏 = 0
  • C π‘Ž = 6 , 𝑏 = βˆ’ 1 2
  • D π‘Ž = βˆ’ 6 , 𝑏 = 0