Question

Complex number help

The complex number w is defined by w = 2 + i.

Shade on an Argand diagram the region whose points represent the complex numbers z which
satisfy
|z − w^2| ≤ |w^2|.

Answer 1

I already found the value of w, that is 3+4i but how to plot it

Answer 2

I mean w^2 is 3+4i

Answer 3

l w^2 l=?

Answer 4

|w^2|=5

Answer 5

oh so you just substitute in?

Answer 6

so u have l z- (3+4i) l <= 5

Answer 7

fine?

Answer 8

why its not
|z − 5| ≤ |5|.

Answer 9

oh i get it

Answer 10

its not |Z-|w||

Answer 11

yes thanks

Answer 12

inside the modulus its w^2 ....not l w^2 l

Answer 13

so how u'll plot this
l z- (3+4i) l <= 5?

Answer 14

circle!

Answer 15

im not sure

Answer 16

okay...z is a complex no...put z= x+iy

Answer 17

i get |z+7-24i|<5

Answer 18

w=2+i then w^2=?
u only told w^2=3+4i

Answer 19

then how it's 7-24 i?

Answer 20

u have squared again....right?

Answer 21

l z- (3+4i) l <= 5

Answer 22

yes from here i square it
|z+7-24i|<5
(z+7-24i)^2<25

Answer 23

on LHS u have l z-w^2 l
and w=2+i

Answer 24

let w^2=3+4i, Z=x+yi
.: |(x+yi)-(3+4i)|<=5 |(x-3)+(y-4)i|<=5

Answer 25

\[\sqrt{(x-3)^2+(y-4)^2} <=5\]

Answer 26

good??

Answer 27

http://openstudy.com/users/akash123#/updates/50853428e4b02a1e48d77eda

Answer 28

LOL hi!!

Answer 29

@Calculator do u get it?

Answer 30

wait

Answer 31

ok i got \[\sqrt{(x-3)^2+(y-4)^2} <=5\]

Answer 32

yes.. keep going

Answer 33

\[(x-3)^2+(y-4)^2 <=25\]

Answer 34

yup so (x=3)^2+(y-4)^2<=5^2 centre with centre (3,4) radius 5

Answer 35

but u only want the points <= the radius

Answer 36

so we can just use
\[\sqrt{(x-3)^2+(y-4)^2} <=5\]
to find the center and radius?

Answer 37

hm? gneeral form of circle is (x-h)^2+(y-k)^2=r^2 where centre at (h,k) and radius of r

Answer 38

ok

Answer 39

do u get

Answer 40

yes

Answer 41

but now i need to draw the circle

Answer 42

btw |z − w^2| ≤ |w^2| you dont need to do algebraically if u dont want to..
if you have |Z1-Z2|=k, that means that the distance from Z1 to Z2 has to equal k.. in this case the distance of Z from the point w^2 has to be constant |w^2|.. you can do just like that

Answer 43

so draw the circle?? midpoint at (3,4)

Answer 44

how about this.. think of it as.. the distance of Z(x,y) from the point 3+4i has to be 5

Answer 45

y7es

Answer 46

so how do you shade?