︠67fade8e-22b4-4b5c-a9f5-a671296cd49cs︠ # 1 z1 = 3 - 2*I z2 = -1 + 2*I z3 = sqrt(2) - I z4 = expand(z3*conjugate(z1-z2)) z5 = expand(conjugate(z1+z3)*(z2-z3)) # Befehlsinfo pretty_print("komplexe Zahl: " + str(z1)) pretty_print("Realteil: " + str(z1.real_part())) pretty_print("Imaginärteil: " + str(z1.imag_part())) pretty_print("Komplex Konjugiert: " + str(z1.conjugate())) pretty_print("Betrag: " + str(z1.abs())) pretty_print("Argument: " + str(arg(z1))) # a) print((z4).real_part()) print((z4).imag_part()) print((z5).real_part()) print((z5).imag_part()) print("") # b) print(abs(z4).full_simplify()) print(arg(z4).full_simplify()) print(abs(z5).full_simplify()) print(arg(z5).full_simplify()) print("") ︡ef10e34c-7ba2-4fc5-a8a0-74888de9102b︡{"html":"
komplexe Zahl: -2*I + 3
"}︡{"html":"
Realteil: 3
"}︡{"html":"
Imaginärteil: -2
"}︡{"html":"
Komplex Konjugiert: 2*I + 3
"}︡{"html":"
Betrag: sqrt(13)
"}︡{"html":"
Argument: -arctan(2/3)
"}︡{"stdout":"4*sqrt(2) + 4\n"}︡{"stdout":"4*sqrt(2) - 4\n"}︡{"stdout":"-4*sqrt(2) - 14\n"}︡{"stdout":"6\n"}︡{"stdout":"\n"}︡{"stdout":"4*sqrt(6)\n"}︡{"stdout":"arctan((sqrt(2) - 1)/(sqrt(2) + 1))\n"}︡{"stdout":"2*sqrt(28*sqrt(2) + 66)\n"}︡{"stdout":"pi - arctan(3/(2*sqrt(2) + 7))\n"}︡{"stdout":"\n"}︡{"done":true}︡ ︠883483f7-a464-4610-8ff6-df3b6f11c7b8s︠ z1 = 3*(cos(225/180*pi())+I*sin(225/180*pi())) z2 = 2*(cos(150/180*pi())-I*sin(150/180*pi())) z3 = 6*exp(2/3*pi()*I) z4 = -4*exp(-5/4*pi()*I) z5 = 3*(cos(45/180*pi())+I*sin(30/180*pi())) z6 = 3*(cos(60/180*pi())-I*sin(150/180*pi())) list_plot([z1, 0], plotjoined=True)+list_plot([z2, 0], plotjoined=True, color='red')+list_plot([z3, 0], plotjoined=True, color='green')+list_plot([z4, 0], plotjoined=True, color='orange')+list_plot([z5, 0], plotjoined=True, color='black')+list_plot([z6, 0], plotjoined=True, color='magenta')+text("z1",(real_part(z1),imag_part(z1)))+text("z2",(real_part(z2),imag_part(z2)))+text("z3",(real_part(z3),imag_part(z3)))+text("z4",(real_part(z4),imag_part(z4)))+text("z5",(real_part(z5),imag_part(z5)))+text("z6",(real_part(z6),imag_part(z6))) ︡4c956bf8-2e2d-4406-a142-9a83f351134e︡{"file":{"filename":"/home/user/.sage/temp/project-356d6df4-33b0-4faf-b59e-8a4b0b2641d6/302/tmp_ZNRRlU.svg","show":true,"text":null,"uuid":"00178fff-8cd1-4634-afee-8428ccd84d79"},"once":false}︡{"done":true}︡ ︠d83735c0-6f5a-4090-8722-a579bb0a559fs︠ z1 = -3/sqrt(2)-I*3/sqrt(2) z2 = -sqrt(3)-I z3 = -3 + I*3*sqrt(3) z4 = 2*sqrt(2)-I*2*sqrt(2) z5 = 3/sqrt(2) + I*3/2 z6 = 3/2 - I*3/2 list_plot([z1, 0], plotjoined=True)+list_plot([z2, 0], plotjoined=True, color='red')+list_plot([z3, 0], plotjoined=True, color='green')+list_plot([z4, 0], plotjoined=True, color='orange')+list_plot([z5, 0], plotjoined=True, color='black')+list_plot([z6, 0], plotjoined=True, color='magenta')+text("z1",(real_part(z1),imag_part(z1)))+text("z2",(real_part(z2),imag_part(z2)))+text("z3",(real_part(z3),imag_part(z3)))+text("z4",(real_part(z4),imag_part(z4)))+text("z5",(real_part(z5),imag_part(z5)))+text("z6",(real_part(z6),imag_part(z6))) ︡c34ffa3f-a74e-4202-94c4-7424071d5b02︡{"file":{"filename":"/home/user/.sage/temp/project-356d6df4-33b0-4faf-b59e-8a4b0b2641d6/302/tmp_ieTCXz.svg","show":true,"text":null,"uuid":"71353151-1de9-4cc6-92aa-89e9959766ba"},"once":false}︡{"done":true}︡ ︠406cbc9c-3e3a-4586-96d8-207ed8364eccs︠ plot(arctan(x),x,-10,10,color="red")+plot(arctan(x)+pi(),x,-10,10,color="green")+plot(+pi()/2,x,-10,10,linestyle="dashed",color="black")+plot(+3*pi()/2,x,-10,10,linestyle="dashed",color="black")+plot(arctan(x)+2*pi(),x,-10,0,color="blue",ticks=[1,pi/2], tick_formatter=[1,pi], axes_labels=['$x$','$\\arctan(x)$']) ︡842b148f-7343-48a6-bb0a-dd90522562aa︡{"file":{"filename":"/home/user/.sage/temp/project-356d6df4-33b0-4faf-b59e-8a4b0b2641d6/136/tmp_QtEv2D.svg","show":true,"text":null,"uuid":"b23918ce-148c-4ec3-8cf3-ce0c4d86229e"},"once":false}︡{"done":true}︡ ︠b332d45e-6fa4-49d5-a142-3375418275bfs︠ z10 = 3*cos(pi()/3)-I*3*sin(5*pi()/6) #(1-I)/sqrt(2) print((z10).real_part()) print((z10).imag_part()) print("") print(abs(z10).full_simplify()) print(arg(z10).full_simplify()) ︡8bb47cf3-7b70-4cbc-bc90-4cedf11cc183︡{"stdout":"3/2\n"}︡{"stdout":"-3/2\n"}︡{"stdout":"\n"}︡{"stdout":"3/2*sqrt(2)\n"}︡{"stdout":"-1/4*pi\n"}︡{"done":true}︡ ︠ca8d3476-1eb3-4553-9623-5196f06ce110︠ z11 = -4*sqrt(2) - 14 + I*6 list_plot([z11,0],plotjoined=true)