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FP1 help PLEASE exam tomorow

a = 3+4i

draw on an argand diagram

mod (z-a) = mod (a) <-----i understand this part, circle

arg(z-3) = arg(a) <---dont understand,
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Avatar for karchun
karchun
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lol.learnt it in lesson this morning :smile: but forget - maybe about the sin(-) and cos(-)...oh yh i remember - u draw it out and its in the first quadrant of the graph and find the (-) of that! so from 0 to say 45 degrees! hope you understood! LOL preping for my own d1 exam next monday - so fking hard...keep getting Cs cuz questions are fking confusing!
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iWarrior
Original post by Freakonomics123
a = 3+4i

draw on an argand diagram

mod (z-a) = mod (a) <-----i understand this part, circle

arg(z-3) = arg(a) <---dont understand,


If you plot the point on an Argand diagram, it'll be (3,4).

Then you need to find the modulus and the argument.

If you draw a line from the origin to the point, the length of that line is the modulus and the angle it makes with the positive x-axis is the argument.

Therefore, by Pythagoras' Theorem, the modulus is the square-root of 3-squared + 4-squared. This means that the modulus will be 5.

Getting the inverse tan of y/x will get you the argument. So it'd be the inverse tan of 4/3, which is 0.927rad.

Therefore you're drawing a circle, centred at (3,-4) with radius 5. And a part-line starting at (3,0), making an angle of 0.927rad with the positive x-axis.

I've got my module today too! Good luck!

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