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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)).
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Practice Questions
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Q1
Find the real part of the complex number z = 4(cos(π/3) + i sin(π/3)).
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4
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The real part is 4 * cos(π/3) = 4 * 1/2 = 2.
Questions & Step-by-step Solutions
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Q
Q: Find the real part of the complex number z = 4(cos(π/3) + i sin(π/3)).
Solution:
The real part is 4 * cos(π/3) = 4 * 1/2 = 2.
Steps: 7
Show Steps
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.
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