Are the real numbers not sufficient? Roots of a polynomial introduction to complex numbers pdf 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.