# Modulus and argument of complex number

**Question**

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

**Answer**

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

*Note:*

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

*|a + bi| = r = √(a ^{2} + b^{2})*

*Argument of the complex number = tan*

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