Question

Complex numbers question: how to show zw and iw on argand diagram...

Answer 1

From the attached picture: i can do a,b,c,d,f but not e or g. please help with the understanding

Answer 2

you know De Moivre's theorem?

Answer 3

yip...

Answer 4

that¡'s what you need here

Answer 5

try to write it in polar form

Answer 6

i, is a complex number with modulus 1 and argument Pi/2
w, also has modulus = 1

Answer 7

so wi = 1*1e^i(Pi/2+argw)

Answer 8

z , looks like it has argument 3Pi/4

Answer 9

got it?

Answer 10

okay so i understand (e) now but i dont understand (g). how would you know where to draw |z||w|

Answer 11

|w|=1, so |zw| will be = |z|, right?

Answer 12

later by De Moivre's theorem, when multiplying complex numbers, their arguments add up. So, like i said, looks like arg(z) = 3Pi/4, so add 3Pi/4 to arg(w), put |zw|=|z| and you are done

Answer 13

the angle arg(z) looks like (3/4)*pi [135 degrees] and arg(w) looks like 240 degrees. So 240 + 135 = 375 = 15 degrees above the x axis. But the answer shows it about 15 degrees BELOW the x axis. Why is this? @myko

Answer 14

@ParthKohli @TuringTest

Answer 15

sorry but two three things I need to learn are complex numbers, combinatorics, and number theory

Answer 16

the three*

Answer 17

I think it should be 15 degrees above the x axis.