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# Imaginary Number convert to exponential form watch

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1. convert to exponential form please

z=(1/2^0.5)(1-i)

2^0.5 is square root of 2

I can't find theta which would satisfy both

[email protected]=-1/2^0.5 and [email protected]=2^0.5

can you tell me how to find the theta please
2. If you have , then . By expanding, you can se that here you have ... I'm sure you can do the rest. Then you have .

Whenever you're finding the argument of a complex number, just remember that
3. thank you
4. (Original post by nuodai)
If you have , then . By expanding, you can se that here you have ... I'm sure you can do the rest. Then you have .

Whenever you're finding the argument of a complex number, just remember that
ok so i get -pi/4 for theta, so z= e^i(-pi/4)

I am also asked to calculate z^(1/4)

I got argument -Pi/16, 31Pi/16.. am I correct so far?

I think numbers are to big, doesn't seem right.
5. (Original post by Sig)
ok so i get -pi/4 for theta, so z= e^i(-pi/4)

I am also asked to calculate z^(1/4)

I got argument -Pi/16, 31Pi/16.. am I correct so far?

I think numbers are to big, doesn't seem right.
Raise the exponential form to 1/4
That means:
r^(1/4).e^(j.#Pi.1/4)
the full stops means multiplication lol

you need to have it in the form r.e^(j.thetha)
the modulus of -> |z| = r which is the square root of x^2 +y^2

refer to the post above if you don't understand because that is in latex form
6. (Original post by carrotboy)
Raise the exponential form to 1/4
That means:
r^(1/4).e^(j.#Pi.1/4)
the full stops means multiplication lol

you need to have it in the form r.e^(j.thetha)
the modulus of -> |z| = r which is the square root of x^2 +y^2

refer to the post above if you don't understand because that is in latex form
YEs I know that and I found 2 of the 4 arguments , above, now can somone tell me if they are correct so far, to me they seem wrong, to bigl...

Thank you
7. isn't too big (or too small)... although I think that it should be . Anyway, you can see it's this by De Moivre's theorem; . You can find the rest of the arguments by adding/subtracting multiples of .

(NB: I could be wrong with some of this, I've only just covered it myself.)

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