What Are the Applications of Complex Numbers in Self-Discovery?

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The discussion emphasizes the importance of conducting preliminary research on complex numbers, specifically regarding their polar form, logarithm, and matrix inversion. Participants suggest that individuals seeking help should demonstrate effort in understanding the problems before asking for solutions. This approach encourages deeper learning and engagement with the material. The thread highlights a common expectation in academic settings for students to attempt problems independently. Overall, self-discovery in mathematics is enhanced through active participation and inquiry.
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This looks like an exam.
 
You should show that you at least tried doing some research on these problems.
For example do some research on polar form of complex numbers, logarithm of complex numbers and inversion of a matrix. Then ask more specific questions, rather than wanting a full solution.
 

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
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