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NAME Q1. (30pts) Solve the quadratic equation z2-(3+3i)z +6+2i = 0 by realizing the following plan: (i) find the discriminant A of the equation; (ii) write a program for a scientific calculator to obtain the polar form r(cos 0 + i sin 0) of A and the 'first' root + isin COS 2 of degree two of A; (iii) execute the program, fix the results, find another root A2 of A of degree two (before executing the program, make sure that your calculat or is set to Radian mode); (iv) find the roots of the quadratic equation. 147 NAME: Q2. (24pts) Consider the curve given in polar coordinates by =-11 cos(0)/sin (0), (00) (i) Make a table of the values of the function f(0)=-11 cos(0)/sin(0) / 2 | 7m/12 | 2m/3 3m/4 5m/6 11m/12 /12 T/6 T/4 T/3 5m/12 f(0) (0, ]; all the values f(0) angle 0, enter the value of 0 to the variable C of your calculator, and then evaluate f(0) using the command -11 x cos Cx (sin C) ; make sure first that your are to be rounded to two decimal places. (Hint. Given on an adian mode). calculator is set (ii) Use (i) to plot the points with polar coordinates (f(0), 0) for all values 0 from table on the graph coordinate paper on the next sheet, and then draw a smooth curve through the plotted points, thereby getting a sketch of the curve. (iii) Use (i) and (ii) to find the area of the region of the plane enclosed by the curve.

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