Question

(z-1)(z *bar -1) can be written as​

Answer 1

Answer:

z - (-2)*bar

Step-by-step explanation:

999999999999

Answer 2

$(z - 1)(\overline{z}-1)= |z - 1|^2 \text{ or } |\overline{z} - 1|^2$  

Given:

$(z - 1)(\overline{z}-1)$

To Find:

Can be written as

Solution:

Z is a complex number and can be represent as x + iy

Z bar  ,   $\overline{Z}=x -iy$

| Z |  = | Z bar | = √(x² + y²)

$(z - 1)(\overline{z}-1)$

(x + iy - 1)(x - iy - 1)

Expand using distributive property

= x² - ixy - x  + ixy  - i²y² - iy  - x  + iy + 1

Using i² = -1    and (-1)(-1) = 1  and cancelling opposite terms

= x² - 2x  + y²  + 1

= ( x - 1)² + y²

=  |z - 1|²

Hence  $(z - 1)(\overline{z}-1)= |z - 1|^2 \text{ or } |\overline{z} - 1|^2$