(iii) A complex number is said to be purely real if Im(z) = 0, and is said to be purely imaginary if Re (z) = 0. The complex number 0 = 0 + i0 is both purely real and purely imaginary.
(iv) Two complex numbers are said to be equal if and only if their real parts and imaginary parts are separately equal i.e. a + ib = c + id implies a = c and b = d. However, there is no order relation between complex numbers and the expressions of the type a + ib < ( or > ) c + id are meaningless.
(v) Since a real number a can be written as a + i.0, therefore every real number can be considered as a complex number whose imaginary part is zero. Thus the set R of real numbers is a proper subset of the complex numbers C.
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