Question

if z=3-2i then show that z^2-6c+13=0 hence find the value of z^4 - 4z^3+6z^2-4z+17​

Answer 1

Given,

z=(2−3i)

z  

2

−4z+13

=(2−3i)  

2

−4(2−3i)+13

=−5−12i−8+12i+13

=−12i+12i−5−8+13

=0

4z  

3

−3z  

2

+2z+170

=4(2−3i)  

3

−3(2−3i)  

2

+2(2−3i)+170

=4(−46−9i)−3(−5−12i)+2(2−3i)+170

=−184−36i−3(−5−12i)+2(2−3i)+170

=−184−36i+15+36i+4−6i+170