1. e² = 1+i. 2. cos z=3+ 4i Determine all complex numbers z such that

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Q: proof heb (a+b)" - {("r) a". b-r

A: To prove that (a+b)n=∑r=0n​(rn​)an−rbr , we will use the Binomial Theorem. Here's the proof:Binomial…

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A: Steps and explanations are as follows:In case of any doubt, please let me know. Thank you.

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A: To find the Laurent series expansion of (z2−1)(z+2)1​  in the annulus  {1<∣z∣<2} , we follow…

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Q: 5. [10 marks] Let G = (V,E) be a graph, and let X C V be a set of vertices. Prove that if |S||N(S)\X…

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Q: Given the system of linear equations 2xyz=1, x-3y+2z = 4, 3x+2y+3z = 5 a) Represent the system as Ax…

A: a ans:Final Solution:x=⎣⎢⎡​xyz​⎦⎥⎤​=⎣⎢⎡​1719​−177​1714​​⎦⎥⎤​.  b ans) Determinant of A and…

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A: Step 1: Step 2: Step 3: Step 4:

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Q: lim 1 x→0x3 3 So²² 6 tln(1+t) t4 +4 .dt 2

A: We need to evaluate:  limx→0​x31​∫0x​t4+4tln(1+t)​dt  Step 1: Consider the Integral for Small t…

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Q: 44 4. Write the function f(x)=2+ ANALYTIC FUNCTIONS 1 (z = 0) Z. in the form f(z) = u(r, 0) + iv(r,…

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