Exam 8: Complex Numbers and Polar Coordinates

Graph the ordered pair on a polar coordinate system. ​

Find 4 fourth roots of . Write each root in standard form. ​

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

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

DeMoivre's Theorem can be used to find reciprocals of complex numbers. Recall from algebra that the reciprocal of x is , which can be expressed as Use this fact, along with DeMoivre's Theorem, to find the reciprocal of the number below.

Find the product. ​

If z is a complex number, show that the sum of z and its conjugate is a real number.

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

Write the complex number in standard form.

Multiply. Leave the answer in trigonometric form. ​

Write the expression  in terms of i .

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

Find x and y (real numbers)so that the equation is true. ​ ​

Write the expression  in terms of i.

Use your graphing calculator to convert the complex number to trigonometric form. Round the angle to the nearest hundredth of a degree.

Solve the equation. ​

Use your graphing calculator to convert to polar coordinates. Round all values to four significant digits. ​

Use your graphing calculator to convert the complex number to trigonometric form. Round the angle to the nearest hundredth of a degree.

Find 4 fourth roots of . Write each root in standard form.

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