Are the real numbers not sufficient? Roots complex numbers polar form pdf a polynomial equation with real coefficients. Are the real numbers not sufficient? To construct a complex number, we associate with each real number a second real number.

We call ‘a’ the real part and ‘bi’ the imaginary part of the complex number. The set of all complex numbers is C. A complex number has a representation in a plane.

The image points of the real numbers ‘a’ are on the x-axis. Therefore we say that the x-axis is the real axis.

Therefore we say that the y-axis is the imaginary axis. We define the sum of complex numbers in a trivial way.

P’ is the vector corresponding with the sum of the two complex numbers. The addition of complex numbers correspond with the addition of the corresponding vectors in the Gauss-plane. We define the product of complex numbers in a strange way. Later on we shall give a geometric interpretation of the multiplication of complex numbers.

Here we see the importance of that strange definition of the product of complex numbers. The real negative number -1 has i as square root! Therefore, the product a .

The only square root of 0 is 0. If a is a strict positive real number, we know that a has two real square roots. It can be proved that there are no other square roots of a in C.