tr-t4n-a

# E r cos θ 4 this is simply the line parallel to the

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= 1. Consequently, its center is at (0,1) and it has a radius equal to 1. (e) r cos( θ )=- 4 This is simply the line parallel to the x-axis defined by x = -4. 2. (10 pts.) Very carefully sketch the graph of the equation x 2 = -4y below. [

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TEST-04/MAC1114 Page 2 of 4 3. (15 pts.) Sketch the given curve in polar coordinates. Do this as follows: (a) Carefully sketch the auxiliary curve, a rectangular graph on the coordinate system provided. (b) Then translate this graph to the polar one. [ See tr-t4g3.pdf. ] Equation: r = 2 cos(2 θ ) (a) r θ (b) y x 4. (10 pts.) Write each expression in the standard forma+b i . (a) (8 - 5i) + (-9 +2i) = -1 - 3i (b) 13/(4 - 3i) = (52/25) + (39/25)i (c) 4i 5 -6 i 7 = 4i -(6)(-i) = 10i (d) (2 - 4i) (-3 + 5i) = 14 + 22i (e) [2(cos 30° + i sin 30°)] 5 =2 5 [cos(150°) + i sin(150°)]
TEST-04/MAC1114 Page 3 of 4 5. (10 pts.) Very carefully sketch the graph of the equation (1/9)x 2 + (1/4)y 2 = 1 below. [ See tr-t4g5.pdf. ] y x 6. (5 pts.) Solve the following equation in the complex number system: x 4 -4x 2 -5=0

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e r cos θ 4 This is simply the line parallel to the x axis...

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