Fsc Part 1 Mathematics (Complete Solution)

Q1
Verify the addition properties of the complex numbers.

SOLUTION:

Let z1=u+vι  ,   z2=w+xι   ,and   z3=y+zι

(i)z1+z2=u+vι+w+xι  

         =(u+w)+(x+v)ι  

thus z1+z2 is a complex no,then the closure law of (+) holds in the set of complex number C.

(ii) (z1+z2)+z3=[(u+vι)+(w+xι )]+(y+zι)

                   = (u+vι)+(w+xι )+(y+zι)

                   = (u+vι)+[(w+xι )+(y+zι)]

                     =z1+(z2+z3)

so (z1+z2)+z3==z1+(z2+z3)

thus it shows that associative law of addition holds in the set of complex numbers C.

(iii)The additive identity in C is (0,0) such that

(x,y)+(0,0) =(x+0,y+0)=(x,y)

so it is hold in the set of complex numbers C.

(iv)Every complex number(x,y) has the additive inverse (-x,-y)  i.e.,

(a,b)+(-a,-b)=(0,0)

 

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