Question

graph |Z-1=2

Answer 1

Z is a complex number?

Answer 2

yeah i mean |Z-1|=2 where Z is part of Complex

Answer 3

If yes, then u have to graph this on Argand plane?

Answer 4

your expretion means: points on complex plane that have distance equal to 2 from point (1,0). Can you finish this now?

Answer 5

yup i know but. why can you view it as distance from two (1,0)? like if you have |Z1-Z2| why is that the distance between Z1 and Z2? what if its |Z1+Z2|?

Answer 6

U have to graph I z- 1I =2, put z=x+iy then u'll come to know

Answer 7

if you treat complex plane like normal xy plane, just instead of x-coordinate and y-coordinate you have real part and imaginary part of a complex number

Answer 8

put z=x+iy then u'll come to know why distance is 2 from (1,0)?

Answer 9

got it?

Answer 10

real numbers (numbers on x axis) will be written like this (n,0). That's why 1 = (1,0)

Answer 11

imaginary numbers (0,n)

Answer 12

yeah i wanna do just by looking at equation no sub points in

Answer 13

so think of it in temr of what modulus means. It's a distance.

Answer 14

yeah what i mean is.. if you have |Z1-Z2|, you take that as distance from Z2 yeah?

Answer 15

yes

Answer 16

ok what if you have |Z+1|=2, centre of circle going to be at (-1,0) because distance from points (-1,0) has to =2 because |Z+1|=|Z--1|

Answer 17

yes

Answer 18

why do you need it to be in the form |Z1-Z2|??

Answer 19

it doesn't need to be in presisly this form. There are many ways to express circle equation. This, probably, is the most easy to see at a glance...

Answer 20

it says that : points Z who's distance from z_0 is constant

Answer 21

Whch means--- circle

Answer 22

|z-z_0|= constant

Answer 23

yes!! but |Z1--Z2| why is difference of 2 points distance from Z2?

Answer 24

one of the points is fixed, other point is generic. It means this other point is changing, with the condition that it's distance to fixed point is constant

Answer 25

yup i understand that.. how about.. why is the fixed point always going to be Z2 in |Z1-Z2| why cant you have |Z1+Z2| the + and -

Answer 26

vector diference:

Answer 27

z1+z2