ALL WORK/WRITING MUST BE YOUR OWN! CONCEPTUAL UNDERSTANDING 1. Show the relation between rotation about the origin by 90 degrees and multiplication by i. Use trigonometry to explain why this relation exists. 2. Given a vector in the complex plane z = a + bi, explain why there are infinitely many complex numbers w such that multiplying z*w results in a Real number. Explain how all of these numbers w are related. . . PROCEDURAL FLUENCY 3. Find the height of the top of the antenna (x) given the two angles of elevation (of 35o and 50o) that were measured from 40m away as shown in the diagram below. 5. Find the area of the triangle △DEF if E = 46o, F = 72o and d = 28cm 6. Find the area of the shaded region .
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