Complex numbers appear often in science and engineering. The suspension of your car, the electronics in your phone, skyscrapers and bridges all use complex numbers in their design.
However, the most important (and interesting) examples are advanced—often appearing in dynamic systems where things change over time. So, when you start learning about complex numbers it can appear that they have little practical use. This is far form true.
parameterize as https://ccrma.stanford.edu/~jos/filters/BiQuad_Section.html
Notch filter determined by a complex number: