The th roots ofz=a+ bi whenk=0, 1, ..., n-1. take the form: 0+2n COS 0+2n +i sin O [cos(0+ 2kx) +i sin(0 + 2ka)] 0+2kn cos 0+2kn +i sin 0+2kn cos 0+2kn +i sin

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Q: Show that there exists a complex number z such that z" +cos(| z |):(1+31z*)=0

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Q: (a-B) show that cosa – cosß = -2sin+P) sin 2 2.

A: We have to show that the following results.  For this we can use some trigonometric results

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Q: 1.) xyax ^)/√²-1²) dx + (x² - 2xy) dy = 0

A: Given : x2-y2dx+x2-2xydy=0 To Check : Differential equation is exact or not

Q: u + (1+ сos u) = 0

A:

Q: Find :L[cos h 5t sin 2t ] 25 2 [(s² – 25)( s² + 4). (s - 5)? +4 O A.) О в) 1 1 1 (s - 5)? +4 (s +…

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Q: If z = +i then Im(coshz) A) –sin1sinh4 B) cos1cosh4 e* +e* C) cos1 2 D) sin1cosh4 E) sin1

A: Topic:- hyperbolic function and complex number

Q: (2) Prove that TT/2 S tane Z coś 0 (1 + tano) ² 11 #la

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Q: Verify the identity. (sec ² 0+1) (- sin² 0+1) = 2-sin ²0 20 rch Which of the following four…

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Q: Find Modulus and arg for: fal tand - (b) 1-Cosx +isind 1+ Sind-i Cosa

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Q: (ez²-1-7²) Sin³z

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Q: (b) Show that: cos(x cos 0) = Jo - 2J₂ cos 20 +2J4 cos 40 +

A: Solution (b):

Q: Evaluate e cosh 2t -3t s13 d) 4(s? - 6s-5) 3. s43 a) 4(s-6s + 5) b) 4(s? + 6s - 5) c) 4(s + 6s +5)

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Q: i) Simplify sin(2sin-1x). ii) Show that sin 30 = 3 sin 0 – 4sin30. iii) By using the substitution 0…

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Q: Find 1+sin -cos I COS In | sin - z+cos In In 1+tan +C +C +C +C

A: We can evaluate the given integral by using the substitution u = tan (x/2).

Q: H-W/ Prove that the Ah root of (-1) are a, ew, awim a w* Since a= cos CF) +i Sin () W= COS (2 )a i…

A: We know that  e^(ix) = cos(x) + i sin(x)  ( cos(x) + i sin(x) )^n = cos(nx) + i sin(nx)

Q: 2. Which of the following is a root of (-1+i)š (a) V2 (cos165° +i sin 165") tbWZfcos65ª+tsimÓS“) (c)…

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Q: Evaluate: e* cos (7e*)cos (4e*) dx (A sin (3e*) +sin (11e") +c - sin (11e*)+C - sin 6. 22 ® -cos…

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Q: -5 cos 2B cos 6B -5 cos 4B + 5 sin 8B -5 cos 8B – 5 sin 4B 2 2 -5 cos 4B – 5 sin 8B -5 cos 4B – 5…

A: Solve : -5cos2Bcos6B Use formula = [cos(a-b)+cos(a+b)]/2

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Q: Show that n. In(cos 2k+2) = - In (2"+ sin 2n+2). k=0 Hint: sin 20 = 2 sin 0 cos 0.

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Q: (s + 1)² + 4 , Select one: O True O False

A: According to our company answering guidelines i can only answer one question if multiple question…

Q: Find the points of intersection between r 2 = 2 cos20 and r =- %3D 1- cose

A: We have to find the intersection between r2=2cos2θ and r=21-cosθ.