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What is the real part of the complex number z = 4e^(iπ/3)?

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Question: What is the real part of the complex number z = 4e^(iπ/3)?

Options:

  1. 2
  2. 4
  3. 2√3
  4. 4√3

Correct Answer: 2√3

Solution: 

The real part is Re(z) = 4 * cos(π/3) = 4 * 1/2 = 2.

What is the real part of the complex number z = 4e^(iπ/3)?

Practice Questions

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

Questions & Step-by-Step Solutions

What is the real part of the complex number z = 4e^(iπ/3)?
Correct Answer: 2
  • Step 1: Identify the complex number given, which is z = 4e^(iπ/3).
  • Step 2: Recall that a complex number in the form re^(iθ) can be expressed using Euler's formula: re^(iθ) = r(cos(θ) + i sin(θ)).
  • Step 3: In this case, r = 4 and θ = π/3.
  • Step 4: To find the real part of z, we need to calculate 4 * cos(π/3).
  • Step 5: Find the value of cos(π/3). The cosine of π/3 is 1/2.
  • Step 6: Multiply 4 by cos(π/3): 4 * (1/2) = 2.
  • Step 7: Therefore, the real part of the complex number z is 2.
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