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    I can do the first part of this question. However the second part has me very confused from the start and the answer makes even less sense to me.

    First how does the exponential come into play? What does the theta represent on the e^?


    Mark scheme says:


    Any assistance is appreciated.
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    (Original post by dominicwild)
    I can do the first part of this question. However the second part has me very confused from the start and the answer makes even less sense to me.

    First how does the exponential come into play? What does the theta represent on the e^?


    Mark scheme says:


    Any assistance is appreciated.

    If you don't understand the exponential form for complex numbers, you could just keep z in the trigonometric form.
    All you do is replace z and then get rid of the imaginary part on the denominator by multiplying the top and bottom by the complex conjugate. After a bit of simplifying, you should be able to show the result.

    Try and do it yourself. If you require any further assistance, just let me know
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    (Original post by dominicwild)
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    \displaystyle e^{i \theta} = \cos \theta + i \sin \theta.

    There are a variety of method you can use to prove this, such as solving the differential equation

    \displaystyle \frac{\mathrm{d}z}{\mathrm{d} \theta} = kz and then show that z = \cos \theta + i \sin \theta is a solution to the differential equation with k=i and using the fact that solutions are unique, that we then have e^{i \theta} = \cos \theta + i \sin \theta.
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    (Original post by razzor)
    If you don't understand the exponential form for complex numbers, you could just keep z in the trigonometric form.
    All you do is replace z and then get rid of the imaginary part on the denominator by multiplying the top and bottom by the complex conjugate. After a bit of simplifying, you should be able to show the result.

    Try and do it yourself. If you require any further assistance, just let me know
    Thanks. I looked up exponential forms of complex numbers and so I now understand where that comes from. I'd never encountered this before, so when it was suddenly thrown out of left field in this question it had me very confused. It was never even mentioned by my lecturer either.

    I also managed to solve it without the exponential form.
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    (Original post by dominicwild)
    Thanks. I looked up exponential forms of complex numbers and so I now understand where that comes from. I'd never encountered this before, so when it was suddenly thrown out of left field in this question it had me very confused. It was never even mentioned by my lecturer either.

    I also managed to solve it without the exponential form.
    There various ways of expressing a complex number; in polar coordinate form (in terms of sin and cos) and the exponential form.
    The relationship between the trigonometric form and the exponential form is known as Euler's formula:
     e^{i\theta} = cos\theta + isin\theta
 
 
 
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