Translation examples
Kompleksiluku z {\displaystyle \scriptstyle z} voidaan esittää karteesisessa koordinaatistossa muodossa z = x + i y , {\displaystyle z=x+iy,} jossa i {\displaystyle \scriptstyle i} on imaginääriyksikkö, tai vaihtoehtoisesti napakoordinaatiston muodossa muodossa z = r ⋅ ( cos θ + i sin θ ) {\displaystyle z=r\cdot (\cos \theta +i\sin \theta )} ja edelleen muodossa z = r e i θ , {\displaystyle z=re^{i\theta },} jossa e {\displaystyle \scriptstyle e} on Neperin luku, kuten Eulerin kaavat osoittavat.
The complex number z can be represented in rectangular form as z = x + i y {\displaystyle z=x+iy} where i is the imaginary unit, or can alternatively be written in polar form (via the conversion formulae given above) as z = r ( cos φ + i sin φ ) {\displaystyle z=r(\cos \varphi +i\sin \varphi )} and from there as z = r e i φ {\displaystyle z=re^{i\varphi }} where e is Euler's number, which are equivalent as shown by Euler's formula.
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