Liczby zespolone.Znaleźć argumenty główne liczb:
a) z=2,
b) z=i
c) z=- Pi
d) z=3-3i
a)
b)
c) z=- Pi - nie wiem jak to zrobić...
d)
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a)![z=2\\ |z|=|2|=2 \\ cos( fi)=\frac{2}{2}=1\\ sin(fi)=\frac{0}{2}=0 \\ (fi)=0 \\ Arg \ z=0 z=2\\ |z|=|2|=2 \\ cos( fi)=\frac{2}{2}=1\\ sin(fi)=\frac{0}{2}=0 \\ (fi)=0 \\ Arg \ z=0](https://tex.z-dn.net/?f=z%3D2%5C%5C+%7Cz%7C%3D%7C2%7C%3D2+%5C%5C+cos%28+fi%29%3D%5Cfrac%7B2%7D%7B2%7D%3D1%5C%5C+sin%28fi%29%3D%5Cfrac%7B0%7D%7B2%7D%3D0+%5C%5C+%28fi%29%3D0+%5C%5C+Arg+%5C+z%3D0)
b)![z=i \\ |z|=\sqrt{1^2}=1\\ cos(fi)=\frac{0}{1}=0 \\ sin(fi)=\frac{1}{1}=1\\ (Arg z=\frac{\pi}{2} z=i \\ |z|=\sqrt{1^2}=1\\ cos(fi)=\frac{0}{1}=0 \\ sin(fi)=\frac{1}{1}=1\\ (Arg z=\frac{\pi}{2}](https://tex.z-dn.net/?f=z%3Di+%5C%5C+%7Cz%7C%3D%5Csqrt%7B1%5E2%7D%3D1%5C%5C+cos%28fi%29%3D%5Cfrac%7B0%7D%7B1%7D%3D0+%5C%5C+sin%28fi%29%3D%5Cfrac%7B1%7D%7B1%7D%3D1%5C%5C+%28Arg+z%3D%5Cfrac%7B%5Cpi%7D%7B2%7D)
c) z=- Pi - nie wiem jak to zrobić...
d)![z=3-3i \\ |z|=\sqrt{3^2+(-3)^2}=\sqrt{9+9}=\sqrt{18}=3\sqrt{2} \\ cos(fi)=\frac{3}{3\sqrt{2}}=\frac{\sqrt{2}}{2} \\ sin(fi)=\frac{-3}{3\sqrt{2}}=-\frac{\sqrt{2}}{2}} \\ Arg z=-\frac{\pi}{4} z=3-3i \\ |z|=\sqrt{3^2+(-3)^2}=\sqrt{9+9}=\sqrt{18}=3\sqrt{2} \\ cos(fi)=\frac{3}{3\sqrt{2}}=\frac{\sqrt{2}}{2} \\ sin(fi)=\frac{-3}{3\sqrt{2}}=-\frac{\sqrt{2}}{2}} \\ Arg z=-\frac{\pi}{4}](https://tex.z-dn.net/?f=z%3D3-3i+%5C%5C++%7Cz%7C%3D%5Csqrt%7B3%5E2%2B%28-3%29%5E2%7D%3D%5Csqrt%7B9%2B9%7D%3D%5Csqrt%7B18%7D%3D3%5Csqrt%7B2%7D+%5C%5C++cos%28fi%29%3D%5Cfrac%7B3%7D%7B3%5Csqrt%7B2%7D%7D%3D%5Cfrac%7B%5Csqrt%7B2%7D%7D%7B2%7D+%5C%5C+sin%28fi%29%3D%5Cfrac%7B-3%7D%7B3%5Csqrt%7B2%7D%7D%3D-%5Cfrac%7B%5Csqrt%7B2%7D%7D%7B2%7D%7D+%5C%5C+Arg+z%3D-%5Cfrac%7B%5Cpi%7D%7B4%7D)