An imaginary number is a complex number that can be expressed in the form of a real number multiplied by the imaginary unit, denoted by the symbol "i". The imaginary unit, i, is defined as the square root of -1. Since there is no real number whose square is negative, the concept of imaginary numbers was introduced to extend the set of real numbers and allow for the solution of equations that involve negative square roots. The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite to the right angle) is equal to the sum of the squares of the lengths of the other two sides. This theorem holds true for both real and complex numbers. The connection between imaginary numbers and [[Pythagorean theorem]] arises when dealing with complex numbers in two-dimensional space. Complex numbers can be represented as points on a complex plane where the real part represents movement along the x-axis, and the imaginary part represents movement along the y-axis. ## An in-depth video tutorial series The Youtube Channel [[Welch Labs]] has a series on [[@welchlabsImaginaryNumbersAre2015|Imaginary numbers are Real]]. # References [[@welchlabsImaginaryNumbersAre2015]]