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# Complex numbers question watch

1. hi

z1 = 2+j

find in the form r (cos0 + jsin0), the complex numerbs z1, z1^2 and z1^3

0 = angle symbol (cnt type it)
2. Do you have any working so far?

If not, first draw an Argand diagram representing , and use trigonometry.

For the second part, do you know De Moivre's theorem? If so, use that. If not, square/cube the number, and draw Argand diagrams again.
3. (Original post by tommm)
Do you have any working so far?

If not, first draw an Argand diagram representing , and use trigonometry.

For the second part, do you know De Moivre's theorem? If so, use that. If not, square/cube the number, and draw Argand diagrams again.
im a little confussed by your method.
can you start me off please for z1?
4. (Original post by SeekerOfKnowledge)
im a little confussed by your method.
can you start me off please for z1?
Do you know what an Argand diagram is?

If not, you can find it in the cos0 + jsin0 form by finding the modulus of z, and then by finding its argument.
5. OK. Can you draw on an Argand diagram? Basically, draw a diagram with an x-axis and a y-axis. The y-axis represents the imaginary part of the number (in this case 1) and the x-axis represents the real part of the number (here, 2). Draw a line from the point where the axes cross to the point (2, 1) representing your number, .

Now, is the angle which your line makes with the positive x-axis (make sure it's in radians, that's important) and is the length of your line. Draw a right angled triangle, and use trig and Pythagoras to find and .

To find , square and repeat the exact same process, drawing an Argand diagram. If you've learnt De Moivre's theorem (which is a bit more advanced), then you could use this, but if you've not, then no matter.
6. (Original post by Rainfaery)
Do you know what an Argand diagram is?

If not, you can find it in the cos0 + jsin0 form by finding the modulus of z, and then by finding its argument.
oh, i just clicked on.

do i meansure the angle anticlockwise
and has r got a value?
7. (Original post by SeekerOfKnowledge)
oh, i just clicked on.

do i meansure the angle anticlockwise
and has r got a value?
r is the modulus. You'll measure how far the angle is from the x-axis. Yours should be tan^-1 (2/1)
8. (Original post by tommm)
OK. Can you draw on an Argand diagram? Basically, draw a diagram with an x-axis and a y-axis. The y-axis represents the imaginary part of the number (in this case 1) and the x-axis represents the real part of the number (here, 2). Draw a line from the point where the axes cross to the point (2, 1) representing your number, .

Now, is the angle which your line makes with the positive x-axis (make sure it's in radians, that's important) and is the length of your line. Draw a right angled triangle, and use trig and Pythagoras to find and .

To find , square and repeat the exact same process, drawing an Argand diagram. If you've learnt De Moivre's theorem (which is a bit more advanced), then you could use this, but if you've not, then no matter.
aha i see,
ive drawn that. but u said is the length of your line it looks more of a diameter to me , doesnt r stand for radius?
9. (Original post by SeekerOfKnowledge)
aha i see,
ive drawn that. but u said is the length of your line it looks more of a diameter to me , doesnt r stand for radius?
I don't understand, what circle is it the diameter of?

r stands for "modulus" although it would represent a radius if were allowed to vary, but I won't go down that route.
10. (Original post by tommm)
I don't understand, what circle is it the diameter of?

r stands for "modulus" although it would represent a radius if were allowed to vary, but I won't go down that route.

lol
oh god, i done it all wrong
ima start again

one last thing, to find the angle in trig, do i do for example sin^-1 4/5
(SOH)?
*need to refresh my memory*
11. Yes, you use SOH CAH TOA, basic trig from GCSE. With complex numbers, you're always going to be using tan, because you're dealing with the opposite (imaginary part) and the adjacent (real part).
12. (Original post by tommm)
Yes, you use SOH CAH TOA, basic trig from GCSE. With complex numbers, you're always going to be using tan, because you're dealing with the opposite (imaginary part) and the adjacent (real part).
oh yeah

thank for your help

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