1. The document is a study guide for a precalculus test that covers topics involving vectors, complex numbers, and their representations and operations. 2. It lists 15 problems involving finding magnitudes and direction of vectors, vector components, dot and cross products, complex numbers in rectangular and polar form, and converting between polar and rectangular coordinates. 3. The problems cover basic vector and complex number calculations, representations, properties and conversions.

1. Precalculus<br />Test 2 Study Guide<br />3657600149860uu1714500149860Magnitude<br />354330085725Resultant<br />194310020955vvScalar<br />Vector<br />1.Find the magnitude and direction of:<br />a) 2vb) v+uc) -v+2ud) 12v-2u<br />2.Find the magnitude of the horizontal and vertical components of v and u.<br />3.a=2, 3, -1 and b=-7,1,-3<br />Write the ordered triple that represents each expression. Find the magnitude of the resultant vector.<br />a) a+bb) -a+2bc) 12a-bd) -b+4a <br />e) 3a+b+2bf) -13b<br />4.Write the vector as the sum of unit vectors. Find the magnitude of each vector.<br />a) 2,4b) -3,5c) -1,3,-2d) 12,3,-8 <br />5.Write the ordered pair or triple that represents YZ.<br />a) Y-2,5, Z2, 8b) Y-1,-5, Z3,7c) Y-4, 12, Z0, -3 <br />d) Y0,6,3, Z1,4,-3 e) Y-2,4,7, Z-3,5,2 <br />6.Find the inner (dot) product of each set of vectors. Are the vectors perpendicular?<br />a) 4,8∙6,-3 b) -6,7,5∙4,9,-3 c) -7,1,0∙4,0,-2<br />7.Find the cross product of each set of vectors. Verify that the resulting vector is perpendicular to the given vectors.<br />a) 4,8,2×6,-3,-1b) 5,-2,5×-1,0,-3c) -2,3,0×5,2,0 <br />8.Prove that for any vector a, a×-a=0<br />9.Use the definition of cross products to prove that for any vectors a, b, c, a×b+c=a×b+a+c<br />10.Graph the following points on the Polar plane.<br />a) 2, 180°b) -1, 3π4c) 3, -45°d) -2,-π6<br />11.Convert the polar coordinates into rectangular.<br />a) 2, 180°b) -1, 3π4c) 3, -45°d) -2,-π6<br />12.Convert the rectangular coordinates into polar.<br />a) -3,4b) (-5,-12)c) 3,-1d) 22,-22<br />13.Solve the equation for x and y. <br />a) 2x+y+xi+yi=5+4i<br />b) 2x-5yi=12+15i<br />c) 1+x+yi=y+3xi<br />14.Write the complex number in polar form.<br />a) -2+4ib) -42c) -1-3id) 6-8i<br />15.Write the complex number in rectangular form.<br />a) 2cos5π4+isin5π4b) cos-π6+isin-π6c) 2.5cos1+isin1<br />16. r represents the ____________ of the complex number.<br />