(а) 23 — 1 (b) z41 (c) 26 = 1 (d) z81 indicate the solutions of each equation on an argand diagram. 10. (a) let a, b be real numbers. find real numbers x and y for which (xyi)2 = a+bi (b) determine the square roots of -7 24i. 11. solve the equations (a) t23t +3 - i= 0 (b) t2(2i 1t+ (5i+ 1) = 0. 12. show that every quadratic equation with complex coefficients has at least one complex root, and therefore can be written as the product of two linear factors with complex coefficients. iz= 1- iz if and only if z is real 13. prove that |1 14. (a) let p(t) be a polynomial with real coefficients. show that, for any complex number w, p(w) = p(w). deduce that, if w is a zero of p(t), then so is w. (b) give a counterexample to show that (a) is not true in general if p(t) has some nonreal coefficients