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Math Help - Write the complex number in rectangular form.

  1. #1
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    Write the complex number in rectangular form.

    Write the complex number in rectangular form. 3cis52degrees ( round to 3 decimal places)
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  2. #2
    MHF Contributor MarkFL's Avatar
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    Re: Write the complex number in rectangular form.

    What does \text{cis}(\theta) mean? What I mean, is use the definition, write it out, then use your calculator to evaluate the trig. functions.
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  3. #3
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    Re: Write the complex number in rectangular form.

    Cis = Cos * i sin
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  4. #4
    MHF Contributor MarkFL's Avatar
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    Re: Write the complex number in rectangular form.

    No, \text{cis}(\theta)\equiv\cos(\theta)+i\sin(\theta).

    So how would you expand 3\,\text{cis}\left(52^{\circ} \right) ?
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  5. #5
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    Re: Write the complex number in rectangular form.

    Wouldn't it be 3*cos52 + 3 * i sin52?
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  6. #6
    MHF Contributor MarkFL's Avatar
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    Re: Write the complex number in rectangular form.

    Yes, that's right, now just use your calculator to approximate the rectangular components. Rectangular form is:

    a+bi where a,b\in\mathbb{R} (i.e. a and b are real.)

    Here we have:

    a=3\cos\left(52^{\circ} \right)

    b=3\sin\left(52^{\circ} \right)
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  7. #7
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    Re: Write the complex number in rectangular form.

    I got 1.847+2.364i as my answer, is that right?
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  8. #8
    MHF Contributor MarkFL's Avatar
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    Re: Write the complex number in rectangular form.

    Yes, that's correct! Good work!
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  9. #9
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    Re: Write the complex number in rectangular form.

    Thank you!
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