Complex numbers as a whole are not a complicated and difficult topic. However, things can get “heated” in less typical and less schematic situations. The key then, as always, is to understand the topic and keep a “cool head,” meaning being clear-headed and confident.
Examples
For example:
- When raising a complex number to some larger power, we often end up with a somewhat strange form like:
To improve the aesthetic of the number, you can perform the following transformation:
Improving aesthetics is often very important – especially if this number is part of an even more complicated mathematical entity. - A complex number in Cartesian (or algebraic) form does not have to be nice looking, for example: . Its real and imaginary parts can be ugly, irrational messes, such as:
But don’t panic, it’s just an ordinary complex number, where (real part not multiplied by ‘i’, imaginary part multiplied):
– changing the sign in the imaginary part
. Its real and imaginary parts can be ugly, irrational messes, such as:
– changing the sign in the imaginary part