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Worksheet: Exponential Form of a Complex Number

Q1:

Put 𝑧 = 5 √ 3 𝑒 πœ‹ 3 𝑖 in algebraic form.

  • A 𝑧 = 5 √ 3 2 βˆ’ 1 5 2 𝑖
  • B 𝑧 = 1 2 + √ 3 2 𝑖
  • C 𝑧 = βˆ’ 5 √ 3 2 + 1 5 2 𝑖
  • D 𝑧 = 5 √ 3 2 + 1 5 2 𝑖
  • E 𝑧 = βˆ’ 1 2 βˆ’ √ 3 2 𝑖

Q2:

Put 𝑧 = 7 𝑒 3 πœ‹ 2 𝑖 in algebraic form.

  • A 𝑧 = 7 𝑖
  • B 𝑧 = βˆ’ 𝑖
  • C 𝑧 = 𝑖
  • D 𝑧 = βˆ’ 7 𝑖

Q3:

Given that 𝑍 = √ 2 𝑖 1 βˆ’ 𝑖 , write 𝑍 in exponential form.

  • A √ 2 2 𝑒 3 πœ‹ 4 𝑖
  • B 𝑒 βˆ’ 𝑖 3 πœ‹ 4
  • C √ 2 2 𝑒 βˆ’ 𝑖 3 πœ‹ 4
  • D 𝑒 3 πœ‹ 4 𝑖

Q4:

Given that 𝑍 = 𝑒 2 βˆ’ 𝑖 5 πœ‹ 4 , find the algebraic form of 𝑍 .

  • A 𝑍 = 𝑒 + √ 2 2 𝑒 𝑖 2 2
  • B 𝑍 = √ 2 2 𝑒 βˆ’ √ 2 2 𝑒 𝑖 2 2
  • C 𝑍 = βˆ’ √ 2 2 𝑒 + 𝑒 𝑖 2 2
  • D 𝑍 = βˆ’ √ 2 2 𝑒 + √ 2 2 𝑒 𝑖 2 2

Q5:

Given that 𝑍 = 𝑒 5 + 𝑖 1 1 πœ‹ 6 , find the algebraic form of 𝑍 .

  • A 𝑍 = 𝑒 βˆ’ 1 2 𝑒 𝑖 5 5
  • B 𝑍 = √ 2 2 𝑒 βˆ’ √ 2 2 𝑒 𝑖 9 9
  • C 𝑍 = √ 3 2 𝑒 + 1 2 𝑒 𝑖 5 5
  • D 𝑍 = √ 3 2 𝑒 βˆ’ 1 2 𝑒 𝑖 5 5

Q6:

Express 1 1 βˆ’ 𝑖 in exponential form.

  • A 1 √ 2 𝑒 βˆ’ 𝑖 πœ‹ 4
  • B 1 2 𝑒 πœ‹ 4 𝑖
  • C 1 2 𝑒 βˆ’ 𝑖 πœ‹ 4
  • D 1 √ 2 𝑒 πœ‹ 4 𝑖

Q7:

Express 𝑍 = βˆ’ 8 in exponential form.

  • A 8 𝑒 0 𝑖
  • B 𝑒 πœ‹ 𝑖
  • C 𝑒 0 𝑖
  • D 8 𝑒 πœ‹ 𝑖

Q8:

Express 𝑍 = βˆ’ 6 in exponential form.

  • A 6 𝑒 0 𝑖
  • B 𝑒 πœ‹ 𝑖
  • C 𝑒 0 𝑖
  • D 6 𝑒 πœ‹ 𝑖

Q9:

Express 𝑍 = 2 in exponential form.

  • A 2 𝑒 πœ‹ 𝑖
  • B 𝑒 0 𝑖
  • C 𝑒 πœ‹ 𝑖
  • D 2 𝑒 0 𝑖

Q10:

Put the number 𝑧 = 5 √ 2 2 βˆ’ 5 √ 6 2 𝑖 in exponential form.

  • A 𝑧 = √ 2 1 0 𝑒 5 πœ‹ 3 𝑖
  • B 𝑧 = 𝑒 5 πœ‹ 3 𝑖
  • C 𝑧 = 5 √ 2 𝑒 2 πœ‹ 3 𝑖
  • D 𝑧 = 5 √ 2 𝑒 5 πœ‹ 3 𝑖
  • E 𝑧 = 5 √ 2 𝑒 1 1 πœ‹ 6 𝑖

Q11:

Put the number 𝑧 = 3 √ 2 βˆ’ 3 √ 2 𝑖 in exponential form.

  • A 𝑧 = 1 6 𝑒 7 πœ‹ 4 𝑖
  • B 𝑧 = 𝑒 7 πœ‹ 4 𝑖
  • C 𝑧 = 6 𝑒 πœ‹ 4 𝑖
  • D 𝑧 = 6 𝑒 7 πœ‹ 4 𝑖
  • E 𝑧 = 6 𝑒 3 πœ‹ 4 𝑖

Q12:

Put the number 𝑧 = βˆ’ √ 3 βˆ’ 3 𝑖 in exponential form.

  • A 𝑧 = √ 3 6 𝑒 4 πœ‹ 3 𝑖
  • B 𝑧 = 𝑒 4 πœ‹ 3 𝑖
  • C 𝑧 = 2 √ 3 𝑒 1 1 πœ‹ 6 𝑖
  • D 𝑧 = 2 √ 3 𝑒 4 πœ‹ 3 𝑖
  • E 𝑧 = 2 √ 3 𝑒 5 πœ‹ 6 𝑖

Q13:

Put the number 𝑧 = βˆ’ 3 √ 2 2 𝑖 in exponential form.

  • A 𝑧 = √ 2 3 𝑒 3 πœ‹ 2 𝑖
  • B 𝑧 = 𝑒 3 πœ‹ 2 𝑖
  • C 𝑧 = 3 √ 2 2 𝑒 πœ‹ 2 𝑖
  • D 𝑧 = 3 √ 2 2 𝑒 3 πœ‹ 2 𝑖

Q14:

Put the number 𝑧 = 7 βˆ’ 7 𝑖 in exponential form.

  • A 𝑧 = √ 2 1 4 𝑒 7 πœ‹ 4 𝑖
  • B 𝑧 = 𝑒 7 πœ‹ 4 𝑖
  • C 𝑧 = 7 √ 2 𝑒 πœ‹ 4 𝑖
  • D 𝑧 = 7 √ 2 𝑒 7 πœ‹ 4 𝑖
  • E 𝑧 = 7 √ 2 𝑒 3 πœ‹ 4 𝑖

Q15:

Put the number 𝑧 = βˆ’ 1 + 𝑖 in exponential form.

  • A 𝑧 = √ 2 2 𝑒 3 πœ‹ 4 𝑖
  • B 𝑧 = 𝑒 3 πœ‹ 4 𝑖
  • C 𝑧 = √ 2 𝑒 5 πœ‹ 4 𝑖
  • D 𝑧 = √ 2 𝑒 3 πœ‹ 4 𝑖
  • E 𝑧 = √ 2 𝑒 7 πœ‹ 4 𝑖

Q16:

Express βˆ’ 8 𝑖 in exponential form.

  • A 8 𝑒 πœ‹ 2 𝑖
  • B 𝑒 βˆ’ 𝑖 πœ‹ 2
  • C 𝑒 πœ‹ 2 𝑖
  • D 8 𝑒 βˆ’ 𝑖 πœ‹ 2

Q17:

Express 4 𝑖 in exponential form.

  • A 4 𝑒 βˆ’ 𝑖 πœ‹ 2
  • B 𝑒 πœ‹ 2 𝑖
  • C 𝑒 βˆ’ 𝑖 πœ‹ 2
  • D 4 𝑒 πœ‹ 2 𝑖