What are complex numbers?
They are more than just real numbers.
Complex numbers fulfill the need to solve for negative square roots. For instance, the equation x2 + 4 = 0 presents with no solution, or false for the calculator, for real numbers. The reason why is that the parabola doesn’t touch the ground or the x-axis.
But simultaneously, the fundamental theorem of algebra disagrees with the “no-solution result.” So, for an exponent of 2, we should expect two results. And the calculator doesn’t plot them because the real numbers don’t arise with enough features to come up with an answer. So even though real numbers accept natural, integers, fractions, rational, and irrational numbers, this system was incomplete.
Complex number’s introduction:
a) z is the letter more often used to describe a complex number.
b) z = a+bi; it is the way the complex numbers present themselves, with a real component (a) + an imaginary component (b), which is always a multiple of √(-1) . The real part and the imaginary part don’t mix. Mathematically speaking, they are not like terms.
The imaginary part example:
√(-3) = √(3) * √(-1)
√(-3) = √(3) i
The √(3) is a real number (R) , and it turns out that (a) and (b) will be real numbers.
c) complex numbers mix counting, algebra, and geometry are the end of the line. There are no more types of numbers.
Complex numbers is used in electromagnetism, classical mechanics, fluid dynamic, and occurs in quantum mechanics, and more interesting, as its includes probabilities the Schrodinger cat invention it is also related to complex numbers.
Fascinating that complex numbers is in the end of the line for types of numbers but at the same time at the beginning to understand the real word around us.
To see more about the History of complex numbers click here