Exam 8: Complex Numbers and Polar Coordinates

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Convert complex numbers to trigonometric form and then simplify the expression. Write the answer in standard form. Convert complex numbers to trigonometric form and then simplify the expression. Write the answer in standard form.

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Find three cube roots for the complex number. Leave your answers in trigonometric form. Find three cube roots for the complex number. Leave your answers in trigonometric form.   ​ ​

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Use a calculator to help write the complex number in standard form. Round the numbers in your answer to the nearest hundredth. Use a calculator to help write the complex number in standard form. Round the numbers in your answer to the nearest hundredth.

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Graph the equation. Graph the equation.   ​ ​

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Use DeMoivre's Theorem to find the following. Write your answer in standard form. Use DeMoivre's Theorem to find the following. Write your answer in standard form.

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Graph the equation using your graphing calculator in polar mode. Graph the equation using your graphing calculator in polar mode.   ​ ​

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Find two square roots for the complex number. Leave your answers in trigonometric form. Find two square roots for the complex number. Leave your answers in trigonometric form.   ​ ​

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Write the equation with rectangular coordinates. Write the equation with rectangular coordinates.   ​ ​

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Write Write    and    in trigonometric form and find their product.     ​  and Write    and    in trigonometric form and find their product.     ​  in trigonometric form and find their product. Write    and    in trigonometric form and find their product.     ​   ​

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Graph the ordered pair on a polar coordinate system. Graph the ordered pair on a polar coordinate system.   ​ ​

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Find two square roots for the complex number. Write your answer in standard form. Find two square roots for the complex number. Write your answer in standard form.   ​ ​

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Write the complex number in trigonometric form. Begin by sketching the graph to help find the argument θ . Write the complex number in trigonometric form. Begin by sketching the graph to help find the argument θ .   ​ ​

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Solve the equation. Leave your solution in trigonometric form. Solve the equation. Leave your solution in trigonometric form.   ​ ​

(Multiple Choice)
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Find three cube roots for the complex number. Leave your answers in trigonometric form. Find three cube roots for the complex number. Leave your answers in trigonometric form.   ​ ​

(Multiple Choice)
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Use your graphing calculator to convert to rectangular coordinates. Round all values to four significant digits. Use your graphing calculator to convert to rectangular coordinates. Round all values to four significant digits.   ​ ​

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Multiply. Leave the answer in trigonometric form. Multiply. Leave the answer in trigonometric form.

(Essay)
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Write the equation with rectangular coordinates. Write the equation with rectangular coordinates.

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Find two square roots for the complex number. Leave your answers in trigonometric form. Find two square roots for the complex number. Leave your answers in trigonometric form.   ​ ​ ​ ​

(Multiple Choice)
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For the ordered pair, give three other ordered pairs with degree values between For the ordered pair, give three other ordered pairs with degree values between   and   that name the same point.   ​     ​  and For the ordered pair, give three other ordered pairs with degree values between   and   that name the same point.   ​     ​  that name the same point. For the ordered pair, give three other ordered pairs with degree values between   and   that name the same point.   ​     ​  ​ For the ordered pair, give three other ordered pairs with degree values between   and   that name the same point.   ​     ​  For the ordered pair, give three other ordered pairs with degree values between   and   that name the same point.   ​     ​  ​ For the ordered pair, give three other ordered pairs with degree values between   and   that name the same point.   ​     ​

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Find the product. Find the product.   ​ ​

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