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If z = 2(cos(π/4) + i sin(π/4)), find |z|.

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Question: If z = 2(cos(π/4) + i sin(π/4)), find |z|.

Options:

  1. 2
  2. √2
  3. 1
  4. 4

Correct Answer: 2

Solution: 

|z| = 2, as |r(cosθ + isinθ)| = r.

If z = 2(cos(π/4) + i sin(π/4)), find |z|.

Practice Questions

Q1
If z = 2(cos(π/4) + i sin(π/4)), find |z|.
  1. 2
  2. √2
  3. 1
  4. 4

Questions & Step-by-Step Solutions

If z = 2(cos(π/4) + i sin(π/4)), find |z|.
Correct Answer: 2
  • 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.
  • Polar Form of Complex Numbers – Understanding the representation of complex numbers in polar form, where z = r(cosθ + isinθ) and |z| = r.
  • Magnitude of Complex Numbers – Calculating the magnitude (or modulus) of a complex number, which is the distance from the origin in the complex plane.
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