8.6+OFSA

OFSA for Complex Numbers
This page contains peer generated questions that help you assess your understanding. Remember that questions may not represent the rigor of the questions you may be expected to complete on formal assessments. This page is simply an OFSA - opportunity for self assessment.


 * Question 1**

Given math x = 3 + 3i math and math y = 1 - i\sqrt {3} math

express x * y in polar form.

math A.\indent ((3\sqrt {2}) + 2)(cis\frac {23\pi} {12}) \\

B.\indent ((6\sqrt {2})(cis\dfrac {23\pi} {12}) \\

C.\indent (\dfrac {3\sqrt {2}} {2}) \(cis(\dfrac {(-17\pi)} {12}) \\

D.\indent ((6\sqrt {2})(cis\dfrac {17\pi} {12}) \\ math

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Given the same x and y from above,
 * Question 2**

Find y/x

math A.\indent (\frac {\sqrt {3}} {3})(cis\frac {17\pi} {12})\\

B.\indent (\dfrac {3} {2})(cis\dfrac {-17\pi} {12})\\

C.\indent (\dfrac {3\sqrt {2}} {2})(cis\dfrac {-17\pi} {12})\\

D.\indent (\dfrac {\sqrt {3}} {3})(cis\frac {23\pi} {12})\\ math

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Using DeMoivre's Theorem, evaluate z^4 for n = {1,2,3,4} math z = \frac {\sqrt {3}} {2} + \frac {i} {2} \\
 * Question 3**

A.\indent z^{4} = 1^{4} (cis(\frac {2\pi} {3})) \\

B.\indent z^{4} = 4(cis(\frac {2\pi} {3})) \\

C.\indent z^{4} = 1^{4} (cis(\frac {4\pi} {3})) \\

D.\indent z^{4} = 4(cis(\frac {4\pi} {3})) \\ math

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math z^{3} = 1+ i math Solve for all solutions math A: z= 2^{\frac{1}{6}}cis(\frac{\pi}{12})
 * Question 4**

B: z= 1^{\frac{1}{6}}cis(\frac{\pi}{12})

C: z=2^{\frac{1}{6}}cis(\frac{\pi}{12}), z=2^{\frac{1}{6}}cis(\frac {3\pi} {4} ), z=2^{\frac{1}{6}}cis(\frac{17\pi}{12})

D: z= 2^{\frac{1}{6}} cis(\frac{\pi}{6}), z=2^{\frac{1}{6}}cis(\frac{\pi}{4}) z=2^{\frac{1}{6}}cis(\frac{2\pi}{3}) math Click here for solution.

math \\ \text{How many solutions are there to this equation and how many of those solutions are expected to be real? } x^{4} =16 \\ \text{A. 4 solutions, 2 real} \\ \text{B. 2 solutions, 2 real} \\ \text{C. 4 solutions, none real} \\ \text{D. 4 solutions, 4 real}
 * Question 5**

math

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math \\ \text{Which of the following is not a complex solution to this equation? } x^{4}=4+4i \\ \text{A.} \indent 4\sqrt{2}cis\frac{\pi}{4} \\ \text{B.} \indent 4\sqrt{2}cis\frac{\pi}{2} \\ \text{C.} \indent 4\sqrt{2}cis\frac{5\pi}{4} \\ \text{D.} \indent 4\sqrt{2}cis\frac{7\pi}{4}
 * Question 6**

math

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math \\ \text{z and w are two complex numbers, and w = 7 + 7sqrt(3)i. If the product of z and w is 140cis(pi/2), what is z in rectangular form} \\ \text{A.} \indent 5+5\sqrt{3}i \\ \text{B.} \indent 5\sqrt{3}+5i\\ \text{C.} \indent 5+5i \\ \text{D.} \indent -5-5i
 * Question 7**

math

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math \text{Given the equation, find the best answer to z to the power of 54: } z=4cis(\frac{2\pi}{3}) \\ \text{A.} \indent (4^5^1)cis(\frac{108\pi}{3})\\ \text{B.} \indent (4^5^1)cis(36\pi)\\ \text{C.} \indent (204)cis(\frac{2\pi}{3}^5^1)\\ \text{D.} \indent (4^5^1)cis(0\pi)\\ math
 * Question 8**

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math \text{ Given } z= \frac{\sqrt{2}}{2}+ \frac{\sqrt{2}}{2}i \text { Convert z into its polar form} \\ \indent \indent \text{ A. } \frac {\sqrt{2}} { 2} cis(\frac{\pi}{4}) \\ \indent \indent \text { B. } 1cis(\frac{\pi}{4}) \\ \indent \indent \text { C, } 1cis(\frac{\pi}{3}) \\ \indent \indent \text { D. } 2cis(\pi) math
 * Question 9**

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math \text { Solve } x^{3} = 27 \text{ for all solutions } \\ math math \indent \indent \text{ A: } 3 \\ math math \indent \indent \text{ B: } 3 \indent -3+ 3\sqrt{3} i \indent 3 - 3\sqrt{3}i \\ math math \indent \indent \text{ C: } 3 \indent \frac {3}{2} + \frac{3\sqrt{3}}{2}i \indent \frac {-3}{2} - \frac{3\sqrt{3}}{2} \\ math math \indent \indent \text{ D: } 3 \indent \frac {-3}{2} + \frac{3\sqrt{3}}{2}i \indent \frac {3}{2} - \frac{3\sqrt{3}}{2} \\ math
 * Question 10**

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 * Question 11**

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 * Question 12**

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 * Question 13**

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 * Question 14**

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 * Question 15**


 * Primary Authors**
 * Chandru Rasendran**
 * Kyle Fredrichs**
 * Thomas Kaszuba**
 * Jay Wang**