Converting the complex number to polar form
1. Martha makes an error converting the complex number to polar form. Where did she make her error? Determine the correct answer and explain what Martha did wrong.
Answer:
(Score for Question 2: ___ of 3 points)
2. David determines that . When he considers the graphical representation of these numbers, he knows he made an error. Clearly explain in complete sentences what David observed, and where David made his mistake. State the correct rectangular equivalence of .
Answer:
(Score for Question 3: ___ of 2 points)
3. Two complex numbers are represented by c + di and , where c, d, e, and f are positive real numbers. In what two quadrants may the product of these complex numbers lie? Explain your answer in complete sentences.
Answer:
(Score for Question 4: ___ of 7 points)
4. What is the product in polar form? In what quadrant of the complex plane does the product lie?
Answer:
(Score for Question 5: ___ of 4 points)
5. Question 3 asked for two possible quadrant locations of the product of c + di and , where c, d, e, and f are positive real numbers. The product in question 4 was two complex numbers of the form c + di and , where c, d, e, and f are positive real numbers. You answered the quadrant location of this product.
Provide an example of two complex numbers in the form c + di and , where c, d, e, and f are positive real numbers such that their product lies in the other possible quadrant. Support your example by determining its product.
Sample Solution
Another technique to represent complex numbers is in their polar form. The rectangular form of a complex number is z = a+bi, where (a, b) are the rectangular coordinates. The modulus and argument of a complex number are used to indicate the polar form of the number. Sir Isaac Newton is credited with creating ten different coordinate systems, one of which being the polar coordinate system.
We will learn how to represent the polar form of complex numbers, the magnitude of complex numbers, the argument of the complex number, and the modulus of the complex number in this mini-lesson.
