# What is a Complex Number?

If we denote A complex number is of the form a + ib where a and b are real numbers.
If z = a + ib, a is the real part of z, denoted by Re(Z) and b is the imaginary part of Z, denoted by Im(Z)
Note:-
1. If the real part of a complex number is zero, then the number is purely imaginary
2. If the imaginary part of a complex number is zero, the number is purely real
3. 0 + 0i represents number 0 in complex number system.
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â€‹Example1. Write the following as complex numbers.

Example 2. Find the real and imaginary parts of the following numbers.

Example 3. Find the real and imaginary parts of
Solution:
i20 = (i4)5 = (1)5 = 1    [Since i2 = -1 and i4 = (i2)2 = (âˆ’1)2 = 1]
i19 = i16.i3 = 1.(âˆ’i) = âˆ’i  [Since i2 = âˆ’1 and i16 = (i2)8 = (âˆ’1)8 = 1, i3 = i2.i = (âˆ’1).i = âˆ’i]