The History of Imaginary Numbers

1. The History of Imaginary Numbers Wilfredo Salazar

2. Gerolamo cardano • In his exposition in 1545,acknowledged the existence of what are now called imaginary numbers. Although he did not understand their properties, mathematical field theory was developed centuries later.

3. An imaginary number • An imaginary number is a number in the form bi where b is a real number and iis the square root of minus one, known as the imaginary unit. • Imaginary numbers and real numbers may be combined as complex numbers in the form a + bi where a and b are the real part and the imaginary part of a + bi. Imaginary numbers can therefore be thought of as complex numbers where the real part is zero. The square of an imaginary number is a negative real number.

4. Geometric interpretation • Geometrically, imaginary numbers are found on the vertical axis of the complex number plane, allowing them to be presented orthogonal to the real axis.

5. Applications of imaginary numbers • For most human tasks, real numbers or even rational numbers offer an adequate description of data. But imaginary numbers have essential concrete applications in a variety of sciences and related areas such as signal processing, control theory, electromagnetism, quantum mechanics, cartography, vibration analysis, and many others.

6. Imaginary numbers are based around mathematical number i which is the square root of -1 • i is defined to be √-1 • i2 = -1 • i3 = i2 * i = -1 * i = - i • i has the following important property • √-a = i√a • Examples • √-3 = √3 *-1= √3 * √-1 = √3* i = i√3 • √-5 = √5 *-1= √5 * √-1 = √5* i = i√5 • √4 = √4 *-1 = √22 * i = 2i