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Which of the following represents the complex number 4 in polar form?

Practice Questions

Q1
Which of the following represents the complex number 4 in polar form?
  1. 4(cos 0 + i sin 0)
  2. 4(cos π/2 + i sin π/2)
  3. 4(cos π + i sin π)
  4. 4(cos π/4 + i sin π/4)

Questions & Step-by-Step Solutions

Which of the following represents the complex number 4 in polar form?
  • Step 1: Understand that a complex number can be represented in polar form as r(cos θ + i sin θ).
  • Step 2: Identify the complex number we are working with, which is 4.
  • Step 3: Determine the modulus (r) of the complex number. For the number 4, the modulus is 4.
  • Step 4: Find the argument (θ) of the complex number. Since 4 is a positive real number, its argument is 0 degrees (or 0 radians).
  • Step 5: Substitute the values of r and θ into the polar form equation: 4 = 4(cos 0 + i sin 0).
  • Step 6: Conclude that the polar form of the complex number 4 is 4(cos 0 + i sin 0).
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