Theory of complex numbers

  • What is the law of complex numbers?

    Following are the arithmetic rules for complex numbers, Addition: For addition of complex numbers, one can write (a + ib) + (c + id) = (a + c) + i(b + d).
    Subtraction: For subtraction of complex numbers, one can write (a + ib) – (c + id) = (a – c) + i(b – d)..

  • What is the principle of a complex number?

    The principal value is simply what we get when we adjust the argument, if necessary, to lie between -π and π.
    For example, z = 2e5 i/4 = 2e-3 i/4, subtracting 2π from the argument 5π/4, and the principal value of the argument of z is -3π/4..

  • Number theory helps to discover interesting relationships between different types of numbers and to prove that they are true.
    Number theory is part experimental and part theoretical.
    The experimental part raises questions and suggests ways to answer them.
Complex numbers allow solutions to all polynomial equations, even those that have no solutions in real numbers. More precisely, the fundamental theorem of algebra asserts that every non-constant polynomial equation with real or complex coefficients has a solution which is a complex number.
The complex number is in the form of a+ib, where a = real number and ib = imaginary number. Also, a,b belongs to real numbers and i = √-1. Hence, a complex number is a simple representation of addition of two numbers, i.e., real number and an imaginary number.

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