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What is the real part of the complex number z = 5e^(iπ/3)?

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Question: What is the real part of the complex number z = 5e^(iπ/3)?

Options:

  1. 5/2
  2. 5/√3
  3. 5√3/2
  4. 5

Correct Answer: 5/2

Solution: 

The real part is Re(z) = 5cos(π/3) = 5 * 1/2 = 5/2.

What is the real part of the complex number z = 5e^(iπ/3)?

Practice Questions

Q1
What is the real part of the complex number z = 5e^(iπ/3)?
  1. 5/2
  2. 5/√3
  3. 5√3/2
  4. 5

Questions & Step-by-Step Solutions

What is the real part of the complex number z = 5e^(iπ/3)?
Correct Answer: 5/2
  • Step 1: Identify the complex number given, which is z = 5e^(iπ/3).
  • Step 2: Recall that a complex number in the form re^(iθ) can be expressed as r(cos(θ) + i sin(θ)).
  • Step 3: Here, r = 5 and θ = π/3.
  • Step 4: To find the real part, we need to calculate 5 * cos(π/3).
  • Step 5: Find the value of cos(π/3). It is equal to 1/2.
  • Step 6: Multiply 5 by 1/2 to get the real part: 5 * (1/2) = 5/2.
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