Worksheet: Exponential Form of a Complex Number

In this worksheet, we will practice converting a complex number from the algebraic to the exponential form (Euler's form) and vice versa.

Q1:

Put 𝑧 = 5 3 𝑒 in algebraic form.

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

Q2:

Express 𝑍 = 8 in exponential form.

  • A 8 𝑒
  • B 𝑒
  • C 𝑒
  • D 8 𝑒

Q3:

Express 8 𝑖 in exponential form.

  • A 8 𝑒
  • B 𝑒
  • C 𝑒
  • D 8 𝑒

Q4:

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

  • A 𝑧 = 2 1 0 𝑒
  • B 𝑧 = 𝑒
  • C 𝑧 = 5 2 𝑒
  • D 𝑧 = 5 2 𝑒
  • E 𝑧 = 5 2 𝑒

Q5:

Given that 𝑍 = 𝑒 , find the algebraic form of 𝑍 .

  • A 𝑍 = 𝑒 + 2 2 𝑒 𝑖
  • B 𝑍 = 2 2 𝑒 2 2 𝑒 𝑖
  • C 𝑍 = 2 2 𝑒 + 𝑒 𝑖
  • D 𝑍 = 2 2 𝑒 + 2 2 𝑒 𝑖

Q6:

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

  • A 2 2 𝑒
  • B 𝑒
  • C 2 2 𝑒
  • D 𝑒

Q7:

Express 1 1 𝑖 in exponential form.

  • A 1 2 𝑒
  • B 1 2 𝑒
  • C 1 2 𝑒
  • D 1 2 𝑒

Q8:

Put 𝑧 = 7 𝑒 in algebraic form.

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

Q9:

Given that 𝑍 = 𝑒 , find the algebraic form of 𝑍 .

  • A 𝑍 = 𝑒 1 2 𝑒 𝑖
  • B 𝑍 = 2 2 𝑒 2 2 𝑒 𝑖
  • C 𝑍 = 3 2 𝑒 + 1 2 𝑒 𝑖
  • D 𝑍 = 3 2 𝑒 1 2 𝑒 𝑖

Q10:

Express 𝑍 = 6 in exponential form.

  • A 6 𝑒
  • B 𝑒
  • C 𝑒
  • D 6 𝑒

Q11:

Express 𝑍 = 2 in exponential form.

  • A 2 𝑒
  • B 𝑒
  • C 𝑒
  • D 2 𝑒

Q12:

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

  • A 𝑧 = 1 6 𝑒
  • B 𝑧 = 𝑒
  • C 𝑧 = 6 𝑒
  • D 𝑧 = 6 𝑒
  • E 𝑧 = 6 𝑒

Q13:

Put the number 𝑧 = 3 3 𝑖 in exponential form.

  • A 𝑧 = 3 6 𝑒
  • B 𝑧 = 𝑒
  • C 𝑧 = 2 3 𝑒
  • D 𝑧 = 2 3 𝑒
  • E 𝑧 = 2 3 𝑒

Q14:

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

  • A 𝑧 = 2 3 𝑒
  • B 𝑧 = 𝑒
  • C 𝑧 = 3 2 2 𝑒
  • D 𝑧 = 3 2 2 𝑒

Q15:

Put the number 𝑧 = 9 2 4 + 9 6 4 𝑖 in exponential form.

  • A 𝑧 = 2 9 𝑒
  • B 𝑧 = 𝑒
  • C 𝑧 = 9 2 2 𝑒
  • D 𝑧 = 9 2 2 𝑒
  • E 𝑧 = 9 2 2 𝑒

Q16:

Put the number 𝑧 = 3 3 𝑖 in exponential form.

  • A 𝑧 = 3 6 𝑒
  • B 𝑧 = 𝑒
  • C 𝑧 = 2 3 𝑒
  • D 𝑧 = 2 3 𝑒
  • E 𝑧 = 2 3 𝑒

Q17:

Express 4 𝑖 in exponential form.

  • A 4 𝑒
  • B 𝑒
  • C 𝑒
  • D 4 𝑒

Q18:

Find the numerical value of 𝑒 + 𝑒 .

  • A 3
  • B0
  • C 3 2
  • D 3

Q19:

Given that 𝑎 𝑒 + 𝑏 𝑒 = ( 2 𝜃 ) 5 𝑖 ( 2 𝜃 ) c o s s i n , where 𝑎 and 𝑏 , find 𝑎 and 𝑏 .

  • A 𝑎 = 2 , 𝑏 = 1
  • B 𝑎 = 2 , 𝑏 = 3
  • C 𝑎 = 2 , 𝑏 = 1
  • D 𝑎 = 2 , 𝑏 = 3

Q20:

Put 𝑧 = 4 3 5 𝜋 6 𝑖 5 𝜋 6 c o s s i n in exponential form.

  • A 𝑒
  • B 4 3 𝑒
  • C 𝑒
  • D 4 3 𝑒
  • E 3 1 2 𝑒

Q21:

Put 𝑧 = 4 3 5 𝜋 6 + 𝑖 5 𝜋 6 s i n c o s in exponential form.

  • A 𝑒
  • B 4 3 𝑒
  • C 4 3 𝑒
  • D 4 3 𝑒
  • E 1 2 𝑒

Q22:

Express the complex number 𝑍 = 𝑒 in exponential form.

  • A 𝑒 𝑒
  • B 𝑒 𝑒
  • C 𝑒
  • D 𝑒 𝑒

Q23:

Put 𝑧 = 6 𝜋 4 + 𝑖 𝜋 4 c o s s i n in exponential form.

  • A 𝑒
  • B 6 𝑒
  • C 𝑒
  • D 6 𝑒
  • E 2 2 𝑒

Q24:

Given that 𝑧 = 2 3 + 2 𝑖 1 and 𝑧 = 2 2 3 𝑖 2 , find 𝑧 𝑧 1 2 , giving your answer in exponential form.

  • A 𝑧 𝑧 = 4 𝑒 1 2 𝑖 3 𝜋 2
  • B 𝑧 𝑧 = 1 6 𝑒 1 2 𝑖 𝜋 6
  • C 𝑧 𝑧 = 1 6 𝑒 1 2 𝑖 4 𝜋 3
  • D 𝑧 𝑧 = 1 6 𝑒 1 2 𝑖 3 𝜋 2

Q25:

Given that 𝑧 = 2 ( 9 0 𝑖 9 0 ) c o s s i n and 𝑧 = 4 ( 3 0 + 𝑖 3 0 ) s i n c o s , find 𝑧 𝑧 , giving your answer in exponential form.

  • A 𝑧 𝑧 = 8 𝑒
  • B 𝑧 𝑧 = 8 𝑒
  • C 𝑧 𝑧 = 8 𝑒
  • D 𝑧 𝑧 = 8 𝑒
  • E 𝑧 𝑧 = 6 𝑒

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.