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A number of the form x + iy, where x, y R, and i = 60114.png is called a complex number and “i” is called iota.
A complex number is usually denoted by z and the set of complex number is denoted by C, i.e.,
C = {x + iy; x R, y R, i = 60108.png}
For example, 5 + 3i, –1 + i, 0 + 4i, 4 + 0i, etc. are complex numbers.


  • For any positive real number a, we have 62779.png.
  • The property 62773.png is valid only if at least one of a and b is non-negative. If aand b are both negative then 62767.png.
  • i4n = 1, i4n + 1 ii4n + 2 = –1, i4n + 3 = –i, where n is any integer.
  • If x and y are two real numbers, then anumber of the form z = x iy is called acomplex number. Here, “x” is called the real part of z and “y” is known as the imaginary part of z. The real part of z is denoted by Re(z) and the imaginary part by Im(z).
  • A complex number z is purely real if its imaginary part is zero, i.e., Im(z) = 0 and purely imaginary if its real part iszero, i.e., Re(z) = 0.

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