Question: (i) Prove that for any complex variable z and complex number a, ( z - a)(z-0*) = z2 -(2Re(a)) z+ lol. (ii) Explain why the

(i) Prove that for any complex variable z and complex number a, ( z - a)(z-0*) = z2 -(2Re(a)) z+ lol. (ii) Explain why the argument 0 of any root a of the equation z' +32 =0 must be of the 2k +1 form n for some integer k and find the common modulus of all the roots of this 5 equation. (iii) Use your results in parts (i) and (ii) to express z' + 32 as a product of one linear factor and two quadratic factors, all with real coefficients. (You may express the coefficients in trigonometric form, where necessary.)

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