Question

if u = -1-sqrt 3i , write vector of u in polar form

Answer 1

you need two things, \(r\) and \(\theta\)

Answer 2

\(r\) is easiest, it is \(r=\sqrt{a^2+b^2}\) which in your case it \[r=\sqrt{1^2+\sqrt{3}^2}=\sqrt{1+3}=\sqrt4=2\]

Answer 3

then you need \(\theta\) where
\[\cos(\theta)=\frac{a}{r}=-\frac{1}{2}\] and
\[\sin(\theta)=\frac{b}{r}=-\frac{\sqrt3}{2}\]

Answer 4

should be clear what \(\theta\) is, then you are done once you write it as
\[r\left(\cos(\theta)+i\sin(\theta)\right)\]

Answer 5

hi thanks for your help, so i'm given an argand diagram should i plot on it the -srt3/2 and -1/2 ?

Answer 6

i guess so
is an "argand diagram" the same as the complex plane?

Answer 7

oh, yes it is
ok right

Answer 8

yeah so are the point above that i mentioned should be drawn?