Figure 1 below shows the complex plane (or Argand diagram
in honour ofJ ohn-Robert Argand), with two real numbers, 3 and -5, two imaginary numbers, i and -2i and four complex numbers, 3 + 4i, -3 + i, -4 - i and 2 - 3i.
On the Argand diagram
mark the position of the point which represents [square root of i].
A two-dimensional graph that plots the real part of a complex number on the x-axis and the imaginary part on the y-axis is commonly called an Argand diagram
The picture we get in this way is called the Argand diagram
Here is certainly the time to introduce the Argand diagram
, and the notation of writing numbers as complex exponentials, along with Euler's identity, complex conjugation and roots of unity; though now students can put to rest any shaky foundations they may have had in this area.
to be an Argand diagram
or, if you prefer, the Complex Plane with the origin at point B.
Roy first gives readers a background in Riemann's zeta function and von Magoldt's work on the xi functions, then turns to theory, explaining basic arithmetic functions, Argand diagrams
, Euler identities, powers and logarithms, the hyperbolic function, standard integration with complex numbers, and line and contour integration.