3 a use Potr form to do the fol ll oving operation Write res

3) a) use Potr form to do the fol ll oving operation Write resvlt in tectangular fo Z,3-3 Zt 2 Solve for all (ots a X\' 80 n the result in rectingvlar tarm

Solution

z1 = 3- 3i ; z2 = -2i

a) z1* z2 = (3 - 3i)(-2i)

= -6i +(-6)

= -6 - 6i

b) z2/z1 = -2i/(3 -3i)

rationalise denominator by multiplying conjugate 3 +3i

= -2i(3+3i)/(9 +9)

=(-6i -6i)/18

= -i/3 -i/3

c) z1^4 = (3- 3i)^4 = (3-3i)^2(3-3i)^2

= ( 9 -9 -18i) (9 -9 -18i)

= -324

x^3 -8 =0

Find the roots : use the formula a^3 - b^3 =(a- b)(a^2 +ab +b^2)

x^3 -8 = (x-2)(x^2 +2x +4) =0

(x-2)(x^2 +2x +4) =0

x = 2

x^2 +2x +4 =0

x= -1 -i*sqrt3 , -1 +i*sqrt3