Numeros imaginarios

TAREA CÁLCULO APLICADO
Multiplicación

r1 =1520°
r2=3040°
rT=1520°3040°=45060°

Demostración

Zt=45060°Zt=450cosα+senβ
Zt=450cos60°+sen60°
Zt=4500.5+i3
Zt=225+2253i
Z2=225+151875i

Z1=1520°
Z1=15cosα+senβ
Z1=450cos20°+sen20°Z1=14.095+5.1303i

Z2=3040°
Z2=30cosα+senβ
Z2=30cos40°+sen40°
Z2=22.9813+19.2836i

Zt=15sin20°+15cos20° 30cos40°+30sin40°Zt=15cos20°30cos40°+15sin20°i30sin40°i+15cos20°30sin40i+15sin20°i30cos40°Zt=15cos20°30cos40°+15sin20°30sin40°i2+15cos20°30sin40i+15sin20°i30cos40°
Zt=15cos20°30cos40°+15sin20°30sin40°-1+15cos20°30sin40i+15sin20°i30cos40°Zt=15cos20°30cos40°-15sin20°30sin40°+15cos20°30sin40i+15sin20°i30cos40°
Zt=225+389.71143i

División:

r1 =645°
r2=315°
rT=645°315°=230°

Demostración

Zt=230°
Zt=2cosα+senβZt=2cos30°+sen30°
Zt=232+12i
Zt=3+i

Z1=645°
Z1=6cosα+senβ
Z1=6cos45°+sen45°
Z1=612+12i
Z1=32+32i

Z2=315°Z2=3cosα+senβ
Z2=3cos15°+sen15°
Z2=36+24+6-24i
Z2=36+324+36-324i

Z2=323+324+323-324i

Z2=323+14+3-14i

321+i323+14+3-14i=1+i3+14+3-14i3+14-3-14i3+14-3-14i=3+14-3-14i2+-3-14i+3+14i3+142+3-14i2 =

3+14-3-14i2+-3-14i+3+14i3+23+116-3-23+116-1 =3+14-3-14(-1)+-3-14i+3+14i3+23+116-3-23+116-1 =3+1+3-14+-3+1+3+14i3+23+116+3-23+116 =23+2i43+23+1+3-23+116 =3+i2816
163+i16= 3+i