zespolona

Zespolona is the feminine form of the Polish adjective zespolony and is used in mathematical terminology to denote something that is complex or composed of parts. In mathematical usage the term appears most often in compound nouns such as liczbа zespolona and płaszczyzna zespolona, referring respectively to a complex number and the complex plane.

Liczba zespolona represents numbers that have a real part and an imaginary part, written in the form z = a + bi, where a and b are real numbers and i is the imaginary unit with i^2 = -1. Each complex number can be mapped to a point (a, b) on the complex plane, a two-dimensional space where the horizontal axis corresponds to the real part and the vertical axis to the imaginary part. Complex numbers are added and multiplied according to standard rules, and they can be expressed in polar form as z = r e^{iθ}, with r = sqrt(a^2 + b^2) and θ the argument of z.

The concept plays a central role in fields such as complex analysis, signal processing, and quantum mechanics. The feminine form zespolona appears regularly in Polish-language texts describing these topics, in phrases like płaszczyzna zespolona (the complex plane) or równania zespolone (complex equations).