--------------- # Aufgabe 1 # --------------- # 1a) Re( (1i)^275 ) Im( (1i)^275 ) # 1b) Re( 1/(1i)^5 ) Im( 1/(1i)^5 ) # 1c) Re( (1i-1)^3 ) Im( (1i-1)^3 ) # 1d) Re( (1+2*1i)/(3-4*1i) ) Im( (1+2*1i)/(3-4*1i) ) # 1e) Re( 1/(1+1i)^2 ) Im( 1/(1+1i)^2 ) --------------- # Aufgabe 2 # --------------- # 2a) Arg(1-1i) Arg(1-1i)/pi # 2b) Arg(-sqrt(3)+1i) Arg(-sqrt(3)+1i)/pi # 2c) Arg( (1-1i)^3 ) Arg( (1-1i)^3 )/pi # 2d) Arg( 2/(1+sqrt(3)*1i) ) Arg( 2/(1+sqrt(3)*1i) )/pi # 2e) Arg( 2/(1i-1) ) Arg( 2/(1i-1) )/pi --------------- # Aufgabe 3 # --------------- z = (4+2*1i)/5 k = 0:100 powers = z^k sn = cumsum(powers) plot(sn) z0 = 1/(1-z) points(z0,col="red",pch="X") --------------- # Aufgabe 4 # --------------- # 4a) dx = 0.01 dy = 0.01 x = seq(from=0,to=0.5,by=dx) y = seq(from=0,to=2.0,by=dy) z = 1i*y plot(z,type="l",xlim=c(-1,1),ylim=c(0,2)) for(k in 1:5) { lines(z+k*0.1) } for(k in 0:20) { lines(x+1i*k*0.1) } # 4b) dx = 0.01 dy = 0.01 x = seq(from=0,to=0.5,by=dx) y = seq(from=0,to=2.0,by=dy) z = 1i*y plot(z^2,type="l",xlim=c(-1,1),ylim=c(0,2)) for(k in 1:5) { lines( (z+k*0.1)^2 ) } for(k in 0:20) { lines( (x+1i*k*0.1)^2 ) } # wenn wir die x-Achse von -4 bis +1 gehen lassen wollen: z = 1i*y plot(z^2,type="l",xlim=c(-4,1),ylim=c(-1,4)) for(k in 1:5) { lines( (z+k*0.1)^2 ) } for(k in 0:20) { lines( (x+1i*k*0.1)^2 ) }