Complex Number


Complex Number definition can be given as numbers that are formed by combination of real numbers and imaginary numbers. It is represented in form of a +ib. Here, ‘a’ is part of real set of numbers and b is  part of imaginary set of numbers. But ‘a’ and ‘b’ are real numbers and ‘I’ is used as an imaginary unit. Values of ‘i’ differ for different values or for different degrees of ‘I’. A complex expression is represented in form of a + ib. Values of ‘i’ is different as i2 is equals to -1, i3 is equals to –I, Similarly, i4 is equals to 1.
If real part of a complex number is zero, then it is said to be purely imaginary number. Similarly, if imaginary part of a complex number is zero then it is said to be purely real number. Different operations can be performed over complex numbers that are two complex numbers can be easily added, subtracted, multiplied and divided. During addition and subtraction, real part of one expression is added and subtracted respectively with real part of second expression and similarly imaginary part of one expression is added and subtracted respectively with imaginary part of second expression. While performing multiplication real and imaginary part of both expressions is multiplied with each other.

When division is performed imaginary part is eliminated from the denominator part by factorizing. It includes multiplication of sign inverse of denominator part with the numerator as well as denominator. Thus, complex numbers definition is all represented in form of real and imaginary combinations of numbers with positive and negative aspects. They can easily verified just by looking at the occurrence of imaginary numbers.

Topics Covered in Complex Number

Complex Plane

There are 2 ways to locate an arbitrary point say A (h, k) in the plane and those are: plotting Cartesian coordinates that are 'h' and 'k' on plane or Polar coordinates are represented as A (r, θ). Complex number plane is a means to represent complex numbers graphically. Like a normal point, complex numbers also have two coordinates. But the difference between l...Read More

Complex Conjugate

Complex Numbers are defined as mathematical numbers with 2 main figures namely Real and Imaginary figures. Classification of complex numbers can be done as either purely real or purely imaginary. But this is not necessary every time. Numbers may be comprised of both real and imaginary parts too. When we say a complex number has only real part, we actually me...Read More

Imaginary Number

Imaginary number is represented by symbol ‘i’. Whenever we use this symbol after a number then number becomes an imaginary number. Basically it is used to find out square root of negative number. We can give ima...Read More

Math Topics