Mathcad - 6 pratybos pdf.mcd

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) f() z = z iz 2 2w = f( x iy)= ( x iy) i ( xiy)= x iyi x 2 2ixy y 2 = x iyix 2 2xy iy 2Re w = x 2xyIm w = y x 2 y 23. Apskaiciuokite ribalimz 1iz 2z 2 z 1 i 2z 2limz 1iz 2z 2 z 1 i 2z 2=00=limz 1i2z 12z 2=2( 1 i) 12( 1 i) 2=2 2i12 2i2=1 2i2i=1 i 12limz 1iz 2z 2 z 1 i 2z 2 1 12 i
4. Apskaiciuokite funkciju reiksmesa) cos( 1 i);b) Ln( 1);c) Ln 1 i ;2sh()ze z e ze z = ch()z =22e zsin( iz) = ish()z cos( iz) = ch()z42cos( αβ) = cos( α) cos( β) sin( α) sin( β)a) cos( 1 i) = cos( 1) cos()i sin( 1) sin()i = cos( 1) ch( 1) isin( 1)sh( 1) 10 5 0 5 10ch(z) 2sh(z) 4 th(z)cos( 1 i) complex cos( 1) cosh( 1) sin( 1) sinh( 1)i 0.834 0.989ib) Ln( z) = { ln|z| i( arg z 2π k) | k ∈ Z }Ln( 1) = ln| 1| i ( arg( 1) 2π k)= i( π 2π k)= πi( 2k 1)k ∈ Zc) Ln1 i2 iarg 1 i 1 iln π1= 2π k= ln( 1) i 2π k = πi 2k k ∈ Z2244 arg1 i2=arctg1212 π= ln 1 i42complex 10simplify 4 πi 0.785iLn( z) ln z i( arg() z 2π k)Ln1 i2π4 i 2πki
Page 4 and 5: 5. Isspreskite lygtisa) sin z =5;3b
Page 6 and 7: 7. Apskaiciuokite ( 1 i) i a b ln
Page 8: ( 1)2 complex cos π2 sin2πi 0

Mathcad - 6 pratybos pdf.mcd

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