Question

已知复数 a=17∠24°.b=6∠－65°.求a+b,a-b,a×b,a÷b

Answer 1

Z(a) = 17(cos24° + i sin24°)
Z(b) = 6(cos65° - i sin65°)
Z(a)+Z(b)=(17cos24°+6cos65°)+i(17sin24°-6sin65°)=(15.53+2.53)+i(6.91-5.43)=18.06+i1.47
Z(a)-Z(b)=(17cos24°-6cos65°)+i(17sin24°+6sin65°)=13+12.34i
Z(a)Z(b)=102(cos24° + i sin24°)(cos65° - i sin65°)=102[(0.3860+0.3686)+i(0.4067-0.8279)
=102(0.7546-0.4212i)=76.96-42.96i
Z(a)/Z(b)=(17/6)(cos24° + i sin24°)/(cos65° - i sin65°)
=(17/6)(cos24° + i sin24°)(cos65°+isin65°)
=(17/6)[(cos24°cos65°-sin24°sin65°)+i(sin24°cos65°+cos24°sin65)
==(17/6)(cos89°+isin89°)