Solve the following problems. be sure to check with your lab/recitation instructor about what is required. will you have to turn in a project report? if so, when will it be due? is there a required format for the report? be clear on what is expected before your group starts to work. this project will give you some practice with complex numbers, review the quadratic formula, and you think geometrically about distances in the complex plane, and makes contact with a curve you know from precalculus or caleulus one route to the quadratic formula: a long time ago in an algebra class you learned the quadratie formula and probably saw how it can be established by completing the square. here is another approach. either one can be used to show that the quadratic formula gives the roots of any quadratie equation az2 +bate 0 whose coefficients may be real or complex mmbers. of course, assume throughout that ? 0. 1. let g be a given complex number. show by the following steps that the eqation-g has exactly two solutions tv where vg stands for one of the solutions. (a) let g rey be a fixed polar form of g. check that vreg where vf is the usual real square root of r. so v -vien/2 is one square root of g (b) check that the identity ' (a + ? ) holds for complex numbers. (c) given the square root in (a) the equation u g can be expressed as w2 ( 0. show that the only solutions of this equation are 2. the quadratic equation a +bs + c = 0 would be easy to solve if b = 0. why? the following steps reduce the solution of a general quadratic to this case. you get to carry them out and rediscover the quadratic formula. (a) let d be a complex number to be deteried. make the change of variable: =? -d in the quadratic equation ct2 + bs + c = 0 to obtain a quadrat equation for (b) what choice of d enables you to reduce the equation for u to one you know how to solve?