Question

If z being a complex number lies on the unit circle and the sum of z with its reciprocal is 1, then find z^235

Answer 1

wt bt this??

Answer 2

z^235? thats alot

Answer 3

theres no answer given bt frm what i know it comes out to be a simple answer

Answer 4

z + 1/z = 1?

Answer 5

yeah

Answer 6

z^2 +1
------- = 1; z^2 +1 = z; z^2 -2 +1 = 0
Z

Answer 7

(z-1)^2; z = 1

Answer 8

z^235 = 1 then ?

Answer 9

but z isnt 1, its a complex number...

Answer 10

typoed it again

Answer 11

z is the 3rd root of -1.
because z^2-Z+1=0;
z^3=1
z^235=z=-1+isqrt(3) /2

Answer 12

z^2+1 = 1

z^2 = 0

z=0 ?

Answer 13

Z^3=-1
(z+1)(z^2-z+1)=0
Z^2-z+1=0;

Answer 14

so that means the the complex part is either up or down

Answer 15

z+1/z=1
z^2-z+1=0.

Answer 16

i think dipankars right, did u apply the demoivres theorem??

Answer 17

no need to apply it....

Answer 18

dip is usually right ;)

Answer 19

i have given the steps....

Answer 20

z is the complex roots of -1.

Answer 21

so but then howdu get z^235??

Answer 22

u must realize amistre m doing wht u often do;)

Answer 23

guess wildly lol

Answer 24

z^235=z^234*z=(z^3*78)^z=1*z=z

Answer 25

no not that...like wht u were doin with the tangent plane question...

Answer 26

ok dipankar....

Answer 27

ahhh... :)

Answer 28

with all the three ;)

Answer 29

its good to be smart :)

Answer 30

him i think u have understood the process...

Answer 31

yeah right...

Answer 32

so, when I find z=0, the complex parts have to be pure imaginaries then right? like "i"

Answer 33

ill tell u what

Answer 34

z + 1/z =1
let z=cosθ + isinθ
1/z = cosθ - isinθ
z + 1/z = 2cosθ = 1
cosθ = 1/2
hence z = 1/2 + √3/2

Answer 35

z^235 = i^235...235/4 = 58 and 3 remaining

i, -1, -1

z^235 = -i?

Answer 36

√3/2 x i sorry

Answer 37

no man
look above
z = 1/2 + i√3/2

Answer 38

lol...stab in the dark then :) i see what you did

Answer 39

now du wanna know the other one as well?

Answer 40

i do, but at this late hour it aint gonna stick to well ;)

Answer 41

hahaha...wts d time there??