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What is the real part of the complex number z = 5e^(iπ/3)?
What is the real part of the complex number z = 5e^(iπ/3)?
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Practice Questions
1 question
Q1
What is the real part of the complex number z = 5e^(iπ/3)?
5/2
5/√3
5√3/2
5
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The real part is Re(z) = 5cos(π/3) = 5 * 1/2 = 5/2.
Questions & Step-by-step Solutions
1 item
Q
Q: What is the real part of the complex number z = 5e^(iπ/3)?
Solution:
The real part is Re(z) = 5cos(π/3) = 5 * 1/2 = 5/2.
Steps: 6
Show Steps
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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