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bulgar [2K]
3 years ago
15

Express the complex number in trigonometric form. -6 + 6 square root of 3 i ?

Mathematics
1 answer:
bagirrra123 [75]3 years ago
5 0
\bf \begin{array}{clclll}
-6&+&6\sqrt{3}\ i\\
\uparrow &&\uparrow \\
a&&b
\end{array}\qquad 
\begin{cases}
r=\sqrt{a^2+b^2}\\
\theta =tan^{-1}\left( \frac{b}{a} \right)
\end{cases}\qquad r[cos(\theta )+i\ sin(\theta )]\\\\
-------------------------------\\\\

\bf r=\sqrt{(-6)^2+(6\sqrt{3})^2}\implies r=\sqrt{36+(6^2\cdot 3)}\implies r=\sqrt{144}
\\\\\\
r=12\leftarrow 
\\\\\\
\theta =tan^{-1}\left( \frac{6\sqrt{3}}{-6} \right)\implies \theta =tan^{-1}\left( -\sqrt{3}\right)\implies \theta =
\begin{cases}
\frac{2\pi }{3}\leftarrow \\
\frac{5\pi }{3}
\end{cases}

now, notice, there are two valid angles for such a tangent, however, if we look at the complex pair, the "a" is negative and the "b" is positive, that means, "x" is negative and "y" is positive, and that only occurs in the 2nd quadrant, so the angle is in the second quadrant, not on the fourth quadrant.

thus         \bf 12\left[cos\left( \frac{2\pi }{3} \right) +i\ sin\left( \frac{2\pi }{3} \right) \right]
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3 years ago
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Andreas93 [3]

Answer:

<u>4-0</u>

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Step-by-step explanation:

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3 years ago
a car decreased in value from $980 to $720 in one year what was the per cent of decrease to the nearest whole per cent ?
kolezko [41]

The decrease was 27%.

Step-by-step explanation:

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New value = $720

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Keywords: Percentage, subtraction

Learn more about subtraction at:

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6 0
3 years ago
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Doss [256]

Answer:

x = 27/5

Step-by-step explanation:

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3 years ago
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Step-by-step explanation:

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Point slope equation is

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Equation of the line in slope intercept form is

y=-1x+1

7 0
3 years ago
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