1−z | ||
Narysować i zaznaczyc zbiory {z∊C: Rez: | =1 | |
1+z |
1−x+yi | ||
Rez | =1 | |
1+x+yi |
1+x | |
=1 | |
1−x |
1+x | 1 | ||
= | |||
1−x | 1 |
1+0 | |
=1 | |
1−0 |
1−x+yi | (1−x + iy)(1+x − iy) | |||
Re [ | ] = 1 ⇔ Re [ | ] = 1 ⇔ | ||
1+x+yi | (1+x +iy)(1+x −iy) |
(1−x+iy)(1+x−iy) | 1−x2+y2+i2xy) | |||
⇔ Re[ | ]=1 ⇔ Re[ | ] = 1 ⇔ | ||
(1+x)2+y2 | (1+x)2+y2 |
1−x2+y2 | 2xy | |||
⇔ Re[ | + i | ] = 1 ⇔ | ||
(1+x)2+y2 | (1+x)2+y2 |
1−x2+y2 | ||
⇔ | =1 | |
(1+x)2 + y2 |