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Modulus and argument of complex number

Question

  1. What are the modulus and argument of 3 + i.
  2. Write down the complex number of 3 + i in the form of r(cos a + sin a*i)

 

Answer

  1. Modulus = √10, Argument = 0.322rad
  2. 2 + 5i = √29(cos 1.57rad + sin1.57rad*i)
Note:

Argument form of a complex number
x + yi = r(cos a + sin a*i)

|a + bi| = r = √(a2 + b2)
Argument of the complex number = tan-1(b/a)

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