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Example Questions
Example Question #26 : Complex Numbers/Polar Form
The following graph represents which one of the following?
Possible Answers:
Correct answer:
Explanation:
The above image is a graphic representation of subtraction of complex numbers (which are represented by vectors and . We can take any complex number and graph it as a vector, measuring units in the x direction and units in the y direction. Therefore . Likewise, .
To help us visualize subtraction, instead of thinking about taking , we should instead visualize . The below figure shows with a dotted line. Visually, the resultant vector lies in between the vectors and . Algebraically, we get or . Either way you think about it, the resulting vector is
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