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

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

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

Steps: 7

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.