Let z 1 5i Calculate the following z2 2 z 1 i z2 iz

Let z = - 1 + 5_i. Calculate the following: z^2 + 2 z + 1 = _+ i z^2 + iz - (-3 + i) = _+ i (z - 5)^2/z + i = _+ i

Solution

solution

z=-1+5i

a)

z²+2z+1= (5i-1)^2+2(5i-1)+1

= 25(i²)+1-10i+10i+1-2

=25i²

^b)

z²+iz-(-3+i)= (5i-1)²+i(5i-1)-(-3+i)

=25i²+1-10i+5i²-i+3-i

=30i²-12i+4

=-(12i+26)

c)

(z-5)²/(z+i)= (5i-1-5)²/(5i-1+i)

= (25i²+36-60i)/(6i-1)

= (11-60i)/(6i-1)