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If z = 2(cos(θ) + i sin(θ)), what is the value of z when θ = π/3?

Practice Questions

Q1
If z = 2(cos(θ) + i sin(θ)), what is the value of z when θ = π/3?
  1. 1 + i
  2. 1 + √3i
  3. 2 + 2i
  4. 1 + 2i

Questions & Step-by-Step Solutions

If z = 2(cos(θ) + i sin(θ)), what is the value of z when θ = π/3?
  • Step 1: Identify the given equation: z = 2(cos(θ) + i sin(θ)).
  • Step 2: Substitute θ with π/3 in the equation: z = 2(cos(π/3) + i sin(π/3)).
  • Step 3: Find the value of cos(π/3). The value is 1/2.
  • Step 4: Find the value of sin(π/3). The value is √3/2.
  • Step 5: Substitute the values of cos(π/3) and sin(π/3) into the equation: z = 2(1/2 + i√3/2).
  • Step 6: Simplify the expression: z = 2 * (1/2) + 2 * (i√3/2).
  • Step 7: Calculate 2 * (1/2) = 1 and 2 * (i√3/2) = √3i.
  • Step 8: Combine the results: z = 1 + √3i.
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