Question

Find the modulus and argument of each root:
i+2 and i-2

Answer 1

lol..is that the continuation of your previous ques ?

Answer 2

Yup

Answer 3

well..i'll explain geometrically..
modulus of a complex number x+iy means the distance of (x,y) from (0,0)
which is => (x^2 + y^2)^1/2
and argument is the angle which the line joining point (x,y) and (0,0) make with positive x axis..
i hope you should again be able to do now..

Answer 4

Still not sure. Which is x and which is y?

Answer 5

coeff of i is y and the other one is x
so in i+2 ,, x=2 and y=1
in i-2 ,, x=-2 and y =1

Answer 6

So \[\sqrt 5\]

Answer 7

and what of argument?

Answer 8

have you learnt about slopes in 2-d geometry ?

Answer 9

Yes, I have.

Answer 10

then you must be able to calculate slope of line joining (x,y) and (0,0) ..
the slope means tan theta..which gives you theta..which is what you want..

Answer 11

I tried for the second one, but I didn't get the correct value...I did for the first though.

Answer 12

I got it. Don't worry.

Answer 13

The last part is to draw an argand diagram, however. How?

Answer 14

Don't worry/

Answer 15

you want me to draw it ? or you got it?

Answer 16

I got it

Answer 17

great then miss emma watson :P !!

Answer 18

how to go about finding the argument for \[(1/2) + i (\sqrt{3}/2)\] ??

Answer 19

calculate the slope of line joining (1/2 , sqrt(3) /2) and (0,0)
slope = tan theta
thus find theta which is the argument..