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If z = 2(cos(π/4) + i sin(π/4)), find |z|.
If z = 2(cos(π/4) + i sin(π/4)), find |z|.
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Practice Questions
1 question
Q1
If z = 2(cos(π/4) + i sin(π/4)), find |z|.
2
√2
1
4
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|z| = 2, as |r(cosθ + isinθ)| = r.
Questions & Step-by-step Solutions
1 item
Q
Q: If z = 2(cos(π/4) + i sin(π/4)), find |z|.
Solution:
|z| = 2, as |r(cosθ + isinθ)| = r.
Steps: 4
Show Steps
Step 1: Identify the given value of z, which is z = 2(cos(π/4) + i sin(π/4)).
Step 2: Recognize that this is in the form of r(cosθ + i sinθ), where r = 2 and θ = π/4.
Step 3: Understand that the magnitude (or absolute value) of a complex number in this form is given by |z| = r.
Step 4: Since r = 2, we can conclude that |z| = 2.
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