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If z = 2(cos(θ) + i sin(θ)), what is the value of |z|?
If z = 2(cos(θ) + i sin(θ)), what is the value of |z|?
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Q1
If z = 2(cos(θ) + i sin(θ)), what is the value of |z|?
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|z| = 2, as |z| = r where z = r(cos(θ) + i sin(θ)).
Questions & Step-by-step Solutions
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Q
Q: If z = 2(cos(θ) + i sin(θ)), what is the value of |z|?
Solution:
|z| = 2, as |z| = r where z = r(cos(θ) + i sin(θ)).
Steps: 5
Show Steps
Step 1: Identify the given expression for z, which is z = 2(cos(θ) + i sin(θ)).
Step 2: Recognize that the expression cos(θ) + i sin(θ) is in the form of Euler's formula, which represents a point on the unit circle.
Step 3: Note that in the expression z = r(cos(θ) + i sin(θ)), r is the magnitude (or modulus) of z.
Step 4: In this case, r is the coefficient in front of (cos(θ) + i sin(θ)), which is 2.
Step 5: Therefore, the magnitude |z| is equal to r, which is 2.
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