Express z_(1)=6+2sqrt3i in polar form. Express your answer in exact terms, using degrees, where your angle is between 0^(@) and 360^(@), inclusive. z_(1)=

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Express  z_(1)=6+2sqrt3i in polar form. Express your answer in exact terms, using degrees, where your angle is between  0^(@) and  360^(@), inclusive.  z_(1)=

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Identify rectangular coordinates: Identify the rectangular coordinates of the complex number. The complex number $ z_1 = 6 + 2\sqrt{3}i $ has a real part (x-coordinate) of 6 and an imaginary part (y-coordinate) of $ 2\sqrt{3} $.Calculate magnitude: Calculate the magnitude (r) of the complex number. The magnitude is given by $ r = \sqrt{x^2 + y^2} $. For $ z_1 $, $ r = \sqrt{6^2 + (2\sqrt{3})^2} $. $ r = \sqrt{36 + 12} $. $ r = \sqrt{48} $. $ r = 4\sqrt{3} $.Calculate argument in radians: Calculate the argument (θ) of the complex number in radians. The argument is given by $ \theta = \arctan\left(\frac{y}{x}\right) $. For $ z_1 $, $ \theta = \arctan\left(\frac{2\sqrt{3}}{6}\right) $. $ \theta = \arctan\left(\frac{\sqrt{3}}{3}\right) $. Since $ \arctan\left(\frac{\sqrt{3}}{3}\right) $ corresponds to $ \frac{\pi}{6} $ radians, we have $ \theta = \frac{\pi}{6} $.Convert argument to degrees: Convert the argument from radians to degrees. $ \theta $ in degrees is given by $ \theta_{deg} = \theta \times \frac{180}{\pi} $. For $ z_1 $, $ \theta_{deg} = \frac{\pi}{6} \times \frac{180}{\pi} $. $ \theta_{deg} = 30^{\circ} $.Express in polar form: Express the complex number in polar form. The polar form of a complex number is given by $ r(\cos(\theta) + i\sin(\theta)) $. For $ z_1 $, the polar form is $ 4\sqrt{3}(\cos(30^{\circ}) + i\sin(30^{\circ})) $.

Express $z_{1}=6+2 \sqrt{3} i$ in polar form. $\newline$ Express your answer in exact terms, using degrees, where your angle is between $0^{\circ}$ and $360^{\circ}$ , inclusive. $\newline$ $z_{1}=$

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Express $z_{1}=6+2 \sqrt{3} i$ in polar form. $\newline$ Express your answer in exact terms, using degrees, where your angle is between $0^{\circ}$ and $360^{\circ}$ , inclusive. $\newline$ $z_{1}=$