Re-express the following complex numbers in the x + iy form: a) z = 3e²(1 + b) z = e(in/4) + In 3 + in)

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Q: Solve the system of congruence 3x + 7y 10 (mod 16) 5x + 2y = 9 (mod 16).

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Q: Let J be a Jordan block. Prove that the Jordan canonical form of the matrix JT is J.

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Q: b) Prove that if f(z) and f(Z) are analytic in a domain I, then I is a constant function.

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Q: 1) Use the limit definition of derivative f'(a) = lim h→0 f(a+h)-f(a) h

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Q: 2. Find the harmonic conjugate v (x, y) of u (x, y) = e cos y + e cos x + xy.

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Q: Show that the Catalan numbers count the following. (a) Sequences (1, 2,..., æn) of positive integers…

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