Difference between revisions of "Talk:2024 AMC 12B Problems/Problem 12"

Revision as of 19:53, 14 November 2024 (view source) Xiaohuang (talk \| contribs) (Created page with "The quadrilateral can be broken down into two triangles: one between z and z^2 and the other between z^2 and z^3. Since the angle between each complex number is the same by De...")		Latest revision as of 08:09, 15 November 2024 (view source) Xiaohuang (talk \| contribs) (Blanked the page) (Tag: Blanking)
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−	The quadrilateral can be broken down into two triangles: one between z and z^2 and the other between z^2 and z^3. Since the angle between each complex number is the same by De Moivre's Theorem, the area of these triangles is 1/2 2 * 4 sin(theta) and 1/2 4 * 8 sin(theta). Thus, 1/2 2 * 4 sin(theta) + 1/2 4 * 8 sin(theta) = 15, and sin(theta) = 15/20 = 3/4. Since the imaginary part of z is equal to \|z\|sin(theta), the imaginary part = 2 * 3/4 = 3/2.	+

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