Radosław Grzymkowski 'MATEMATYKA Zadania I Odpowiedzi' Strona34 Liczby Zespolone

334 27. Liczby zespc.

334 27. Liczby zespc.

27.5.

27.6.

27.7.

27.8.

27.9.

*    _    1 _T    3 _    1    3    [2    ^

a) Re z = -, Im z = z = - + -t, |z| = y-. b) Re z = _:

13    1    [2

Imz = —-, z = - + -i, Izj =    a/ . c) Rez =    O,    Imz -    -

o    5    5    V 5

z = i, |z| = 1. d) R.ez = —1, Imz = 2, z = — 1 — 2ż, |z| =

3

e) Rez = 0, Imz = -8, ź = 8i, \z\ = 8. f) R.ez = -, Imz =

3    3\/2

z = -(1 4- ż), \z\ = —. g) Rez = —2, Imz = 2, ź = — 2 - 1

jz| = 2\/2. h) Rez = —16, Imz = 8, z = —16 — 8i, \z\ = 8\ :l i) Re z = 6, Imz = —8, z = 6 +    8i, \z\ — 10.

a) Re z = —1, Im z = 0, z = 1,    |z| = 1. b) R.ez = 2,    Imz =    — 1.

z — 2 + i, jz| = \/5. c) R.ez = 188, Imz = —74,    z = 188 +    "4:

jzj = v^/40820.

a) |zj = 2, Arg z = — ^ + 2kn, k £ C, argz = —^. b) |z| = 3\ .

3    3    7r

Argz = -7r + 2&7r, A: G C, argz = -ir. c) |z| = x/2, Argz = —\-2k~

4    4    4

7T    7    —

k £ C, arg z — —. d) |z| = \/2, Arg z = -7r+2/c7r, k £ C, arg z = —

e) jz| = 4, Argz = 7T + 2A;7r, k £ C, argz = 7r. f) |zj = 7

Argz = I+2/ctt, A: G C, argz = g) |z| = Argz = -^ + 2A“ k £ C, arg z = — —. h) |z| = 1, Arg z = ~ + 2A:7t, k £ C, arg z = -

a) |z| = 16, R.ez — 16, Argz = 2kn, k £ C, argz = 0. b) jz| = 32. Rez =    —32,    Argz    =    ^    +    2kn,    A;    G    C,    argz    =    c)    |z|    =    64.

R.ez =    64,    Argz    =    2A:7r,    ł    G    C,    argz    =    0.    d) |z| = 8,    R.ez    =    G

7T    7T

Arg z = — + 2k.TT_y k £ C, arg z = —.

a)    z = 4 (cos(7r + 3x) + i sin(7r + 3x)), x £ (—17r, 0).

b)    z = 32 ^cos ^-7r + 2m^ + isin ^7r + 2x^, x £ (— |7r, — ^7r).

^c)    ^z = 7, (cos (^ + 2x^j + isin (^ + 2x^, x £ (—|tt, J).