Precalculus : Polar Coordinates and Complex Numbers

Study concepts, example questions & explanations for Precalculus

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Example Questions

Example Question #7 : Find The Roots Of Complex Numbers

Determine the length of 

Possible Answers:

Correct answer:

Explanation:

, so  

Example Question #8 : Find The Roots Of Complex Numbers

Solve for all possible solutions to the quadratic expression:

 

Possible Answers:

Correct answer:

Explanation:

Solve for complex values of m using the aforementioned quadratic formula: 

Example Question #9 : Find The Roots Of Complex Numbers

Which of the following lists all possible solutions to the quadratic expression: 

Possible Answers:

Correct answer:

Explanation:

Solve for complex values of  using the quadratic formula: 

Example Question #10 : Find The Roots Of Complex Numbers

Determine the length of .

Possible Answers:

Correct answer:

Explanation:

To begin, we must recall that . Plug this in to get . Length must be a positive value, so we'll take the absolute value: . Therefore the length is 3.

Example Question #21 : Powers And Roots Of Complex Numbers

Solve for  (there may be more than one solution).

Possible Answers:

Correct answer:

Explanation:

To solve for the roots, just set equal to zero and solve for z using the quadratic formula, which is 

 and now setting both  and  equal to zero we end up with the answers  and  and so the correct answer is .

Example Question #11 : Find The Roots Of Complex Numbers

Solve for all possible solutions to the quadratic expression: 

Possible Answers:

Correct answer:

Explanation:

Solve for complex values of  using the quadratic formula: .

Example Question #23 : Powers And Roots Of Complex Numbers

Solve for  (there may be more than one solution).

Possible Answers:

Correct answer:

Explanation:

To solve for the roots, just set equal to zero and solve for  using the quadratic formula ():  and now setting both  and  equal to zero we end up with the answers  and .

Example Question #1 : Express Complex Numbers In Rectangular Form

Convert the following to rectangular form:

  

Possible Answers:

Correct answer:

Explanation:

Distribute the coefficient 2, and evaluate each term: 

Example Question #2 : Express Complex Numbers In Rectangular Form

Convert the following to rectangular form:  

Possible Answers:

Correct answer:

Explanation:

Distribute the coefficient and simplify:

Example Question #3 : Express Complex Numbers In Rectangular Form

Represent the polar equation:

in rectangular form.

Possible Answers:

Correct answer:

Explanation:

Using the general form of a polar equation:

we find that the value of  is   and the value of  is .

The rectangular form of the equation appears as , and can be found by finding the trigonometric values of the cosine and sine equations. 

distributing the 3, we obtain the final answer of:

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