The “imaginary” number i is defined as the square root of –1. ... But using the expanded form—the right side of Taylor’s equation—helps ... e ix = cos x + i sin x. When Euler set x ...

With the polar form of complex numbers established, the matter of Euler’s Identity is merely a special case of a+bi for a = -1 and b = 0. Consequently for the polar form re iφ , this makes r ...

To a nonmathematician, having the letter “i” represent a number that does not quite exist and is “imaginary” can be hard to ...

Euler’s identity: Math geeks extol its beauty, even finding in it hints of a myste­rious connected­ness in the universe. It’s on tank tops and coffee mugs. Aliens, apparently, carve it into ...

Euler’s formula relies on imaginary numbers. Raina Okonogi-Neth. Calculus becomes easier, too. As mathematicians Roger Cotes, René Descartes – who coined the term “imaginary number ...