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anonymous

  • one year ago

HOW is anybody supposed to find the answer to this pre calc question???? Express the complex number in trigonometric form. -2 How am i supposed to do anything with that number? These are my choices, but I am completely lost! : 2(cos 90° + i sin 90°) 2(cos 0° + i sin 0°) 2(cos 180° + i sin 180°) 2(cos 270° + i sin 270°)

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  1. anonymous
    • one year ago
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    z = |z|(cos Θ + i sin Θ) For yours z = -2 + 0i, so |z| = 2. The real part is the horizontal axis, so Θ = 0°

  2. anonymous
    • one year ago
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    you could check the answer choices, which would be one way

  3. anonymous
    • one year ago
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    not to disagree with @peachpi but for \(-2\) you would have \(\theta=\pi\) or if you are working in degrees for some unknown reason \(\theta=180^\circ\)

  4. anonymous
    • one year ago
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    |dw:1439175703750:dw|

  5. anonymous
    • one year ago
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    What is that formula called? @peachpi

  6. anonymous
    • one year ago
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    oh yeah. forgot about the negative

  7. anonymous
    • one year ago
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    it is not a formula, it is an equality between numbers \[2(\cos(180)+i\sin(180))=2\times (-1+0)=-2\]

  8. anonymous
    • one year ago
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    Ah, okay. Im getting 2(cos 0° + i sin 0°) as my answer

  9. anonymous
    • one year ago
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    but that cannot be correct since \(\cos(0)=1\) not \(-1\)

  10. anonymous
    • one year ago
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    Im still a bit confused on the process of getting to my answer...

  11. anonymous
    • one year ago
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    @satellite73

  12. anonymous
    • one year ago
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    it is an equality between two numbers you have \(-2\) right?

  13. anonymous
    • one year ago
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    the absolute value of \(-2\) is \(2\)

  14. anonymous
    • one year ago
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    Right @satellite73

  15. anonymous
    • one year ago
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    therefore it will be \[2(\cos(\theta)+i\sin(\theta))=-2\] which is only possible if \(\sin(\theta)=0\) since \(-2\) has no \(i\) in it and if \(\cos(\theta)=-1\) since \(2\times -1=-2\)

  16. anonymous
    • one year ago
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    so one possible value of \(\theta\) is \(180\) as \(\cos(180)=-1\) and \(\sin(180)=0\)

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