Find the real part of the complex number z = 4(cos(π/3) + i sin(π/3)).

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Question: Find the real part of the complex number z = 4(cos(π/3) + i sin(π/3)).

Options:

Correct Answer: 2

Solution:

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

Find the real part of the complex number z = 4(cos(π/3) + i sin(π/3)).

Find the real part of the complex number z = 4(cos(π/3) + i sin(π/3)).

Correct Answer: 2

Step 1: Identify the complex number z given in the question, which is z = 4(cos(π/3) + i sin(π/3)).
Step 2: Recognize that the real part of a complex number in the form a(cos(θ) + i sin(θ)) is given by a * cos(θ).
Step 3: In this case, a = 4 and θ = π/3.
Step 4: Calculate cos(π/3). The value of cos(π/3) is 1/2.
Step 5: Multiply the value of a (which is 4) by cos(π/3): 4 * (1/2).
Step 6: Perform the multiplication: 4 * (1/2) = 2.
Step 7: Conclude that the real part of the complex number z is 2.

Complex Numbers – Understanding the representation of complex numbers in polar form and how to extract real and imaginary parts.
Trigonometric Functions – Knowledge of the values of trigonometric functions, specifically cosine and sine, at standard angles.