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If z = 2(cos(π/3) + i sin(π/3)), find z in rectangular form.

Practice Questions

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

Questions & Step-by-Step Solutions

If z = 2(cos(π/3) + i sin(π/3)), find z in rectangular form.
  • Step 1: Identify the given expression for z, which is z = 2(cos(π/3) + i sin(π/3)).
  • Step 2: Calculate cos(π/3). The value of cos(π/3) is 1/2.
  • Step 3: Calculate sin(π/3). The value of sin(π/3) is √3/2.
  • Step 4: Substitute the values of cos(π/3) and sin(π/3) into the expression for z: z = 2(1/2 + i√3/2).
  • Step 5: Distribute the 2 into the expression: z = 2 * (1/2) + 2 * (i√3/2).
  • Step 6: Simplify the expression: z = 1 + √3i.
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