Number Sets

Complex Number

Number that can be written in the form a + bi where a and b are real numbers and i2 = −1.
In this kind of notation, the number a is called the real part and the number b is called the imaginary part of the complex number. The set of real numbers is a subset of the set of complex numbers. We write this as: [latex]\mathbb{R} ⊂ \mathbb{C}.[/latex] The set of imaginary numbers is a subset of the set of complex numbers.

Examples

  • The number [latex]\sqrt{-16}[/latex] is a complex number, because: [latex]\sqrt{-16}[/latex] = 0 + 4i.
  • The number 25 is a complex number, because: 25 = 25 + 0i.

Historical Note

If i2 = −1, then: i = [latex]\sqrt{-1}[/latex]. and we can write: [latex]\sqrt{-16}[/latex] = 0 + 4i = 0 + 4[latex]\sqrt{-1}[/latex] The symbol [latex]\sqrt{-1}[/latex] appeared for the first time in the notes of Leonhard Euler (1707-1783), published in 1794.

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