If z = 1 + I, then Z-2 / (the square of Z)=

If z = 1 + I, then Z-2 / (the square of Z)=

z=1+i
z²=2i
(z-2)/z²
=(-1+i)/2i
=(-i-1)/(-2)
=(1+i)/2

If z = 1 / (2 + I), then | Z|=

Multiply up and down by 2-I
z=（2-i）/5
So | Z | = the root of five is five

The real part of complex z = (1 + I / 2) ^ 15 greatly helps to write the calculation process, thank you
The real part of complex z = (1 + I / 2) ^ 15
Greatly help write about the calculation process, thank you

Module length r = sqrt (5) / 2, argument a = arctan (1 / 2) of complex u = 1 + I / 2
So the module length of Z = (1 + I / 2) ^ 15 = R ^ 15 = 5 ^ {7 / 2} / 2 ^ 7, and the argument of Z = (1 + I / 2) ^ 15 = 15A
So the real part = 5 ^ {7 / 2} / 2 ^ 7cos (15a) = 5 ^ {7 / 2} / 2 ^ 7cos (15arctan (1 / 2))

What is the minimum of | Z + 1 / 2 | + | Z-6 |
The condition is | Z | = 1, not - | Z | = 1!

When z = 1, | Z + 1 / 2 | + | Z-6 | = 6.5
When z = - 1, | Z + 1 / 2 | + | Z-6 | = 7.5
So when z = 1, the minimum value of | Z + 1 / 2 | + | Z-6 | is 6.5