tożsamość trygonometryczna
: 2 gru 2012, o 01:25
\(\displaystyle{ \left| \frac{z}{\left| z\right| } \right|=1}\)
\(\displaystyle{ z=|z|(\cos \alpha + i \sin \alpha)}\)
\(\displaystyle{ z=|z|(\cos \alpha + i \sin \alpha)}\)
\(\displaystyle{ \blue \left| \frac{z}{\left| z\right| } \right|=1}\)
\(\displaystyle{ z=|z|(\cos \alpha + i \sin \alpha)}\)
\(\displaystyle{ \left| \frac{z}{\left| z\right| } \right|=\left| \frac{|z|(\cos \alpha + i \sin \alpha)}{\left| z\right| } \right|=\left|\cos \alpha + i \sin \alpha\right|=\sqrt{\cos^2\alpha+\sin^2\alpha}=\sqrt{1}=\ \red 1}\)