dan150999
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#1
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write the complex number

z = 2e^(2i.pi/3) - e^(-i.pi/3) in its exponential form

what do I do? thanks
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ghostwalker
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#2
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(Original post by dan150999)
write the complex number

z = 2e^(2i.pi/3) - e^(-i.pi/3) in its exponential form

what do I do? thanks
I suggest drawing the two numbers on a diagram, and hopefully it will then be obvious.
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David Getling
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(Original post by dan150999)
write the complex number

z = 2e^(2i.pi/3) - e^(-i.pi/3) in its exponential form

what do I do? thanks
It might help to remember that the first number is 2(cos(2π/3) + isin(2π/3)
and the second number is cos(-π/3) + isin(-π/3).
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RDKGames
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(Original post by dan150999)
write the complex number

z = 2e^(2i.pi/3) - e^(-i.pi/3) in its exponential form

what do I do? thanks
This is the same as

e^{i\frac{2\pi}{3}}[2 - e^{-i\frac{3\pi}{3}}]


...notice anything ??
Last edited by RDKGames; 3 weeks ago
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David Getling
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(Original post by RDKGames)
This is the same as

e^{i\frac{2\pi}{3}}[2 - e^{-i\frac{3\pi}{3}}]


...notice anything ??
Even if the OP prefers what I showed, this kind of factorization may well be needed in other questions, and should definitely be mastered.
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dan150999
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(Original post by RDKGames)
This is the same as

e^{i\frac{2\pi}{3}}[2 - e^{-i\frac{3\pi}{3}}]


...notice anything ??
lol no another clue please? still don't get it.
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RDKGames
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(Original post by dan150999)
lol no another clue please? still don't get it.
What does e^{-i\frac{3\pi}{3}} simplify to?
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dan150999
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#8
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(Original post by RDKGames)
What does e^{-i\frac{3\pi}{3}} simplify to?
-1?
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RDKGames
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(Original post by dan150999)
-1?
Yep
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dan150999
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(Original post by David Getling)
It might help to remember that the first number is 2(cos(2π/3) + isin(2π/3)
and the second number is cos(-π/3) + isin(-π/3).
this is how far I got when I did it. But when I add them together it still doesn't give me the correct answer so I'm going wrong somewhere with the addition
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David Getling
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(Original post by dan150999)
this is how far I got when I did it. But when I add them together it still doesn't give me the correct answer so I'm going wrong somewhere with the addition
Did you convert this to numbers first? It's absolutely essential that you know the cos and sin values of things like π/6, π/4 and π/3, and your CAST diagram.
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