FourfundannentaloperationsAdditive rulesz+w=w+zz+(w+s)=(z+w)+sz+0=z+ (-2) = 0Multiplication ruleszw=wz(zw)s = z(ws)1z=zz(z-1)=1 for z0Distributive rulez(w+s)=zw+zssha Uni. of Sci&Tech)FCV&ITSeptember2,20198/40MineLilChal
Four fundamental operations Additive rules z + w = w + z z + (w + s) = (z + w) + s z + 0 = z z + (−z) = 0 Multiplication rules zw = wz (zw)s = z(ws) 1z = z z(z −1 ) = 1 for z 6= 0 Distributive rule z(w + s) = zw + zs Ming Li (Changsha Uni. of Sci & Tech) FCV & IT September 2, 2019 8 / 40
FourfundaentaloperationsCompute2+3i13.(2)(1)2-3isha Uni. of Sci & Tech)FCV&ITSeptember2,20199/40MineLlCha
Four fundamental operations Compute (1) i 3 , (2) 2 + 3i 2 − 3i Answer: (1) − i, (2) −5 + 12i 13 Ming Li (Changsha Uni. of Sci & Tech) FCV & IT September 2, 2019 9 / 40
FourfundantaloperationsCompute2+3i3(1) (2)2-3iAnswer:-5 + 12i(2)(1)-i13tha Uni.ofSci&Tech)FCV&ITSeptember2,20199/40MineLilCha
Four fundamental operations Compute (1) i 3 , (2) 2 + 3i 2 − 3i Answer: (1) − i, (2) −5 + 12i 13 Ming Li (Changsha Uni. of Sci & Tech) FCV & IT September 2, 2019 9 / 40
FourfunLoneations1.2GeometricrepresentationofcomplexnumbersaUni.ofSci&Tech)FCV&ITSeptember2.201910/40MineLilCh
Four fundamental operations §1.2 Geometric representation of complex numbers Ming Li (Changsha Uni. of Sci & Tech) FCV & IT September 2, 2019 10 / 40
ceometric reoresentation of comolexnumbersGeometricrepresentationof complexnumbersImaginaryaxis(yaxis),z=a+bi0Real axis (r axis)vectorrepresentation:z=a+ibFCV&ITsha Uni.of Sci &Tech)September2.201911/40MineLlchs
Geometric representation of complex numbers Geometric representation of complex numbers O Real axis (x axis) Imaginary axis (y axis) z = a + bi θ r r cos θ r sin θ vector representation: z = a + ib triangle functions representation: z = r(cos θ + isin θ) polar coordinate representation: z = re iθ Ming Li (Changsha Uni. of Sci & Tech) FCV & IT September 2, 2019 11 / 40