In each case, write the function

f(z)

in the form

f(z)=u(x,y)+iv(x,y)

:\ (a)

f(z)=z^(3)+z+1

;\ (b)

f(z)=(/bar (z)^(2))/(z),(z

)

!=

(

0)

.\ Suggestion: In part (b), start by multiplying the numerator and denominator by

/bar (z)

.\ Ans. (a)

f(z)=(x^(3)-3xy^(2)+x+1)+i(3x^(2)y-y^(3)+y)

;\ (b)

f(z)=(x^(3)-3xy^(2))/(x^(2)+y^(2))+i(y^(3)-3x^(2)y)/(x^(2)+y^(2))

.

In each case, write the function f(z) in the form f(z)=u(x,y)+iv(x,y) : (a) f(z)=z3+z+1; (b) f(z)=zz2(z=0). Suggestion: In part (b), start by multiplying the numerator and denominator by z. Ans. (a) f(z)=(x33xy2+x+1)+i(3x2yy3+y); (b) f(z)=x2+y2x33xy2+ix2+y2y33x2y