1. 2. Realne funkcije realne varijable - FESB
1. 2. Realne funkcije realne varijable - FESB
1. 2. Realne funkcije realne varijable - FESB
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Racunske operacije s kompleksnim brojevima<br />
Neka su z 1 = x 1 + iy 1 ; z 2 = x 2 + iy 2 2 C; deniramo:<br />
z 1 + z 2 = x 1 + x 2 + i (y 1 + y 2 ) ;<br />
z 1 z 2 = x 1 x 2 + i (y 1 y 2 ) ;<br />
z 1 z 2 = (x 1 + iy 1 ) (x 2 + iy 2 ) =<br />
= x 1 x 2 + ix 1 y 2 + iy 1 x 2 + i 2 i<br />
y 1 y 2 1<br />
2 =<br />
= x 1 x 2 y 1 y 2 + (x 1 y 2 + y 1 x 2 ) i;<br />
z 1<br />
z 2<br />
= x 1 + iy 1<br />
x 2 + iy 2<br />
= x 1 + iy 1<br />
x 2 + iy 2<br />
x 2 iy 2<br />
x 2 iy 2<br />
=<br />
= x 1x 2 ix 1 y 2 + iy 1 x 2 y 1 y 2 i 2 i 2 1<br />
x 2 2 y2 2 =<br />
i2<br />
= x 1x 2 + y 1 y 2<br />
x 2 2 + y2 2<br />
+ y 1x 2 y 1 y 2<br />
x 2 2 + y2 2<br />
i za z 2 6= 0:
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