Solve the integral [e³+4x sin 2x dx using complex numbers.

Q: Find the three cube roots of -8i.

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Q: Consider the complex number z = (1 – i)(-1-iv3). Find |2| and arg(2).

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Q: •b+ci k dz z2 + 2yz + y? a

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Q: Extract the square root of the complex number 8-6i.

A: We have to find the square root of the complex number 8-6i.

Q: Use the trigonometric form of a complex number to show that z-n = 1/zn , where n is a positive…

A: To prove the given identity

Q: Find the roots, including the complex ones, of 2x³– 3x? = 1 using Newton's method.

A: To find the roots using Newton's method, 2x3-3x2=12x3-3x2-1=0Let, f(x)=2x3-3x2-1…

Q: Solve the complex number z = (2+3i)^3/2

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Q: Find all the complex roots of (6−6i)^(1/7) .

A: To find all the complex roots of 6-6i17, we shall use De Moivre's formula.

Q: Find the product in the complex plane 1/4(cos Pi/6 +i sin pi/6) + 8 (cos pi/6 + i sin pi/6)

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Q: Write the complex number z=(1-√3i)2015/(√2cis(7π/6))4028 in an exponential form.

A: cis(x) = cos(x)+isin(x)

Q: Simplify the complex power [(1+i)/(1-i)]-2i  and leave your answer in its simplest form.

A: Use the following formulae, to obtain the solution.…

Q: 88 11% COSX + dx cakulate using complex functions?

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Q: f(x) = Jsinx 02x>N T >x22n

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Q: Find the value of x in the complex equation (2x - 3yi)(3 + 4i) = 78 - 21i %3D

A: Given complex equation (2x-3yi)(3+4i)=78-21i To determine the value of x  First multiple left hand…

Q: Find the value of y in the complex equation (2x-3yi(3 + 4i) 78-21i O5 -3 03 -4

A: Given, (2x-3yi)(3+4i)=78-21i Expanding the LHS⇒ (2x-3yi)(3+4i)=6x+8xi-9yi-12yi2…

Q: Find the 5 fifth roots of -4+5i.

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Q: Solve using complex analysis: 1²t Jo 5-4cos(0) 2 cos(30) -do

A: Given: ∫02πcos3θ5-4cosθdθ. We have to solve using complex analysis.

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Q: find the 4th root of z=2i-3

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Q: 1 s(? + z)) z + i +8) dz, where C is the circle |z + i| = 1, 0 < t < 2m

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