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  1. 1Sine of 7π/6
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  12. 12Solving tanx=√3
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  14. 14Law of sines for a side
  15. 15Law of cosines, finding a side
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  21. 21Logs: solving log equation
  22. 22Solving ln(2x+1)=3
  23. 23Solving 2^(x+1)=3^x
  24. 24Solving exponential growth
  25. 25Solving a cubic by factoring
  26. 26Remainder theorem
  27. 27Roots of a cubic
  28. 28Asymptotes of a rational function
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  30. 30Arithmetic sequence term and sum
  31. 31Geometric sequence, 8th term and sum
  32. 32Sum of infinite geometric series
  33. 33Vector magnitude and dot product
  34. 34Angle between two vectors
  35. 35Resolving a force vector
  36. 36Multiplying complex numbers
  37. 37Dividing complex numbers
  38. 38Quadratic with complex roots
  39. 39Modulus and argument of z

39Modulus and argument of z

Find the modulus and the argument (in degrees) of z = 1 + √3 i.

The modulus |z| = 2 and the argument θ = 60°. Using |z| = √(a² + b²) = √(1² + (√3)²) = √4 = 2, and θ = tan⁻¹(√3/1) = 60° since the point lies in the first quadrant. Check: 2cos60° = 1 and 2sin60° = √3.

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