Let Z1 and Z2 be roots of the equation z + pz + q = 0, where the coefficients p and q may be complex numbers. Let A and B represent z₁ and z2 in the complex plane, respectvely. If ZAOB = 0#0 and OA = OB, where O is the origin, prove that p² = 4q cos² (8/2). 2

Q: [9-R] [CLO 7] Let z = 4 − 3i be a complex number. Determine zz.

A: given z=4-3i be a complex number

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A: Please see the below picture for detailed solution.

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A: Let's find.

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Q: 1. Let z and w be complex numbers. (a) Show that |1+ z w² + |z – w2 = (1+|z|?)(1+ |w/?). (b) Show…

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A: Let z = x + yi, where x and y are real numbers. Then, we can write a^z as:   a^z = a^(x+yi)

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