复杂的number:
A number in the type of x + iy, where x, y are real numbers and i = √-1 is known as a complex number.
(i) Normally
for an integer n.
(ii) If z = x + iy, then the real part of z is shown by Re (z) and the imaginary part denoted by Im(z).
(iii) A complex number is called purely real if Im(z) = 0, and is called simply imaginary if Re (z) = 0. The complex number 0 = 0 + i0 is both only real and only imaginary.
(iv) Two complex numbers are called similar if and only if their imaginary parts and real parts are separately same i.e. a + ib = c + id means a = c and b = d. but, there is no order relation in between complex numbers and the relation of the complex no a + ib < ( or > ) c + id are meaningless.
(v) Since a real number a may be defined as a + i.0, therefore each and every real number may be defined as a complex number whose imaginary part is zero. Therefore the set R of real numbers is a proper subset of the given complex numbers C.
Remark:Clearlyfor an integer n.
Representation of complex numbers in argand plane:
A complex number z = x + Iy defined as ordered pair (x, y) may be shown by a point P whose Cartesian coordinates are (x, y) submitted to axes OX and OY, generally known as the imaginary and the real axes. The plane of OY and OX is known as the complex plane or Argand diagram. |
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