1. true or false. justify your answer. (a) |x+iy| ≤ |x| + |y| (b) arg(-2+10i) = π – tan−¹(5) + 2nπ for n an integer.

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A: Given:- To differentiate:-

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A: solution of the given question is like aS:

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A: Recall the following formula  ln(a+bi)= ln √(a²+b²) + i tan-1(b/a) .

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A: Here is the solution:

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A: In this problem, simple substitution formula is used to solve the integration

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A: We have to show                            ∫01x1+x22dx=∫0π42sin2θdθ     by substituting  x=tan2θ and…

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A: Since you have posted multiple question in this question so I have solved first question as per our…

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Q: x sin(x? – 1) Vcos(x² – 1) +

A: Given that: ∫-11xsin(x2-1)cos(x2-1)+13dx

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A: please see the next step for solution

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A: Using sine wave graph we can find it easily

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A: Given that, the functions are fx=12cos2x+1-6 and gx=-1. Equate the functions to find the solution x…