Complex Number

Complex number

Introduction:

Consider a simple quadratic equation x2 + 1 = 0. There is no real number which satisfies this equation. So there was a need to find a system which could answer to this problem. Euler used the symbol 'i' to denote to solve the above equation.

Complex number system consists of the set of all ordered pairs of real numbers (a, b) denoted by a + ib, where i =
Complex number

Square root of a negative number is known as an imaginary number.

If x and y are real numbers, then x + iy is called a complex number. x is called the real part and y is called the imaginary part.

The following are the types of complex numbers: Equality of Complex numbers, Sum of two Complex numbers, Negative of a Complex number, Additive identity of the Complex number, Additive inverse of a Complex number, Product of two Complex numbers, Multiplicative identity of Complex numbers, Conjugate complex numbers, Quotient of two non-zero Complex numbers, Reciprocal of a non-zero complex number or multiplicative inverse of a non-zero complex number.
Properties of Complex numbers

The Properties of Complex numbers are:Commutative Law for Addition, Commutative Law for multiplication, Additive Identity Exists, Multiplicative Identity Exist, Reciprocals (Multiplicative Inverses) Exist for nonzero complex numbers, Negatives (Additive Inverses) Exist for all complex numbers, Non Zero Product Law.
Graphical representation of Complex numbers

The complex number Z = x + iy may be represented graphically by the point P whose rectangular co-ordinates are (x, y)। Thus each point in the plane is associated with a complex number.