What is complex number

Aug 09, 2022, 16:45 IST

About Complex Number

The complex quantity is essentially the mixture of a true number and an complex number. The complex quantity is within the sort of a+ib, where a = real and ib = complex number. Also, a,b belongs to real numbers and that i = √-1. Hence, a complex number may be a simple representation of addition of two numbers, i.e., real and an complex number. One a part of it's purely real and therefore the other part is only imaginary.

Properties of Complex Numbers

i. If z = a + ib, then the important a part of z is denoted by Re (z) and therefore the imaginary part of a complex number by Im (z).

ii. A complex number is claimed to be purely imaginary if Re (z) = 0.

iii. A complex number is claimed to be purely real if Im(z) = 0.

iv. The complex quantity 0 = 0 + i0 is both purely real and purely imaginary.

v. Two complex numbers are said to be equal if and as long as their real parts and imaginary parts are separately equal i.e., a + ib = c + id implies a = c and b = d.

vi. However, there's no order relation between complex and therefore the expressions of the sort a + ib < (or >) c + id are meaningless.