Question

Complex number questionsss :(

Answer 1

i dont even know how to start on (i). theres no W but the question ask to find W.
or should it suppose to be W = -2iz ?

Answer 2

do they mention a W earlier in the text?

Answer 3

no they didnt..

Answer 4

post their solution. maybe we can "reverse engineer" what they mean

Answer 5

ok

Answer 6

heres the solution.. but after reading it i still dun understand =.=

Answer 7

and im a independent student.. so i have no teacher.. my only teacher is openstudy xD

Answer 8

It looks like a typo, and they meant
w= -2iz

Answer 9

Looks you have a First edition textbook with all printing mistakes >.<

Answer 10

yea i thought so too ><..

Answer 11

can i know how does |-2i| = 2?

Answer 12

basically the question is about figuring out how the angle changes when you multiply a complex number by a pure imaginary number

Answer 13

also, they are pretty sloppy about w vs \(w_1\)

\[ i= \cos(\pi/2) + i \sin(\pi/2) = e^{i \frac{\pi}{2}} \]

Answer 14

think of |-2i| as |0-2i|

Answer 15

heard of "iteration in complex plane" before @HatcrewS

Answer 16

erm.. nope.. only know the vectors.. :S

Answer 17

and -2i is
\[ -2 e^{i \frac{\pi}{2}} \]

we should notice that -2 = \( 2 e^{i \pi} \)
so that we have
\[ 2 e^{i \frac{3\pi}{2}} \]
match that with
\[ M e^{i \theta} \]
M is 2

Answer 18

or as ganeshie points out, in rectangular form
a+bi, M= sqr(a^2 + b^2)

here
-2i is 0 - 2 i and we get sqr(0+4)= 2

Answer 19

ooh.. |z| = r = sqr(x^2 + y^2)

Answer 20

yes

Answer 21

just to add to that, notice below when u multiply something by \(z\) :
1) multiiplying a "real number" by \(z\) changes the magnitude but never the angle
2) multiplying a "imaginary number" by \(z\) changes the angle

overall : you need some imaginary part to rotate in complex plane :
\(zi\) changes the angle of \(z\) by 90 degrees ccw
\(-zi\) changes the angle of \(z\) by -90 degrees ccw

Answer 22

everytime you multiply \(i\), the vector gets rotated by 90 degrees ccw

Answer 23

multiplying a "imaginary number" by z changes the angle . does it change the magnitude too ?

Answer 24

ccw means what clockwise ? anti clockwise ?

Answer 25

ccw = counter clock wise

opposite of your regular clock

Answer 26

if the number has mag≠ 1 , multiplying will change the product's length.

Answer 27

ohh.. i know it as anti clockwise xD

Answer 28

lets take a complex number, multiply \(i\) and see what exactly happens :)