Question: Work out thoroughly each question on complex numbers 1. A quadratic equation is given by ax + bx + c = 0, where a, b,

Work out thoroughly each question on complex numbers

1. A quadratic equation is given by ax + bx + c = 0, where a, b, c E R. The complex roots of the equation are a = 1 - 3i and B. (a) Calculate (a + B) and (aB). (b) Hence, find the equation, with integer coefficients, with roots - and 1 a - 2 B - 2 [6] 2. A complex number v = x + iy is such that v2 = 2 + i. Show that x2 - 2+ v5 2 [7]

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