<img src="https://tex.z-dn.net/?f=%20-%201%20%2B%20%20-%202" id="TexFormula1" title=" - 1 + - 2" alt=" - 1 +

Anarel [89]

3 years ago

ddle" class="latex-formula">

Mathematics

1 answer:

MissTica3 years ago

6 0

Answer:

-3

Step-by-step explanation:

Basically it's like if you owe a dollar (-1), and then you owe 2 more dollars (-2), now you owe 3 dollars (-3).

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Find the complex fourth roots \[-\sqrt{3}+\iota \] in polar form.

____ [38]

Let $z=-\sqrt3+i$ . Then

$|z|=\sqrt{(-\sqrt3)^2+1^2}=2$

$z$ lies in the second quadrant, so

$\arg z=\pi+\tan^{-1}\left(-\dfrac1{\sqrt3}\right)=\dfrac{5\pi}6$

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$z=2e^{i5\pi/6}$

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$2^{1/4}e^{i(5\pi/6+k\pi)/4}$

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$2^{1/4}e^{i(5\pi/6+2\pi)/4}=2^{1/4}e^{i17\pi/24}$

$2^{1/4}e^{i(5\pi/6+4\pi)/4}=2^{1/4}e^{i29\pi/24}$

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