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

Q: (cose – sin0)² = 1 – 2sin@cos0 %3D

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Q: find all complex Values satisfy ing the given equation ē = 2+1 (-1+i) .

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Q: Can you write the product of a sum or difference of 16sin(29b)sin(16b) ?

A: The objective of the question is to express the product of two sine functions, 16sin(29b) and…

Q: Express the number -5 in the form R(cos(0) + i sin(0)) = Reil where R>0 and 0 <0 < 2T.

A: rewrite -5 as -5=-5+0i comparing with z=a+bi a=-5 , b=0 R=a2+b2=-52+02=25+0=25=5 now…

Q: Rewrite the complex number 3(cos 3.5 + i sin 3.5) in a + bi form a = b =

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Q: Verify the identity: cos2 x - sin2 x = 2 cos2 x - 1

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Q: Express as a product. sin 4ẞ + sin 10ẞ + sin 22ẞ + sin 16ẞ

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Q: Evaluate sin²(7#6 + 2e'®) de. 2n Jo

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Q: 2 1 + cos2x can be simplified to: O sin²x O csc² x O cos²x O sec² x

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Q: - Z= 5(cos60° + jsin60°) (7/40°) (6-j5)-4e-j5

A: The given problem is to evaluate and simplify the given complex expression.

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

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Q: Evaluate these complex numbers: (a) _2 – j] (b) 6 30° + j5 –- 3 + e45°

A: To find- Evaluate these complex numbers:  j31 + j2 - j2 6∠30° + j5 - 3 + ej45°

Q: use demoirvre's Theorem of powers z= Square root 2 (cos 5 pi/24 +i sin 5 pi/24)

A: Given : z=2cos5π24+isin5π24 de moivre's theorem: If z=rcosθ+isinθ then zn=rncosnθ+isinnθ.

Q: Please show full work! Thank you

A: we have to slove above question the product of cos (5t)sin(8t)

Q: + jsin 12 12 .2 +jsin - Simplify 3 cos cos

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Q: Verify that (¹)² = i²i but that (i²)i ‡ į²i ("i" imaginary unit)

A: What is Complex Number: A real number and an imaginary number are effectively combined to create a…

Q: do Evaluate the intergal using the 12 + 8 sin 0 residue theorem.

A: The general form of a complex number is given by z=a+ib, where a,b are two real numbers and i=-1.…

Q: #5

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Q: How does (2cos(theta))2 + (-2sin(theta))2 equal 4?

A: 2cosθ2+-2sinθ2=4cos2θ+4sin2θNext step:-

Q: Given the complex numbers z = 2 + j3,zz = -1 - j2,andzg=4+j4 find; Im (高)x+x@zs)+Im(zz+z) (元)

A: Given: Complex numbers are z1=2+j3, z2=-1-j2 and z3=4+j4. To find:…

Q: 0.5e-1.94 in the rectangular form z = a + jb. Express the complex number z = Enter your answers…

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Q: -1+5i -i

A: topic- complex numbers  real part is added and subtracted with real part and imaginary part is added…

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.

Q: Simplify the following: 3+7i 1. (4 + 2i) + (–3 – 51) 2. (–3 + 4i) – (5+ 2i) in standard form 3.…

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