The complex equation wn = z have solutions in the form of wm=r1/n (cos((θ+2πm)/n) + i sin ((θ + 2πm)/n)) where r = |z|           θ = arg(z)           m is an integer Show that wn+k = wk for integer k. The equation can only have n solutions

Q: Q1\ Answer only two of the following questions: A\ Evaluate f sinx esecx cos²x dx. [15] [8 4 3 1 B\…

A: We have to solve the given problems.

Q: Determine the fifth roots of z = (4-j5)cos(1+j3). Express your answer in rectangular form

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Q: Use m = =√₁m [cos (m² (0 + 2kπ)). + 2kx)) + i sin in((0 + 2kx))] to find all solutions of the…

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Q: Solve the equation: (D² - 1) y = 0 Oy=c₁e* + c₂xe* + c3 cos x + c4 sinx Oy=c₁e¹* + c₂e + c3 cos x +…

A: A detailed solution is given below.

Q: 5a. sinx + cos2x Write general solutions for each equation given in Part a.

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Q: If a = cos (2ñ/7) + i sin (27/7), then find the quadratic equation whose roots are a = a + a² + a²…

A: If  a=cos 2π7+isin2π7, then we have to find the quadratic equation whose roots are   α=a+a2+a4  and…

Q: The roots of a d.e are -1, 2+√3 What is the solution? y = ex(c₁ cos 3x + c₂ sin 3x) + c3 cOS X + C4…

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Q: 1. (a) Find the roots of the equation 23 + 2 – 2/3i = 0.

A: Here we have to find the roots of z3+2-23i=0. For that consider z3+2-23i=0⇒z3=-2+23i. Finding the…

Q: Solve for A +능 D %3D B If: A=V8 (Cos ti Sin) %3D 8 = (1+i) c : V2+2i D = 3[2.5 cis los°- 3.3 cis 60]

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Q: B)Convert r = √2 cos(0-) to cartesian.

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Q: The complex numbers sin x +i cos 2x are conjugate to each other for (a) x = nt (b) x = 0 (c) x = (n…

A: on based data given detailed solution provided

Q: Find all solutions of the following equationsa a)z/1-z=1-5i   b) (2-i)z+8z^2=0.  c)z^4-16=0

A: a). z1-z = 1 - 5i⇒ z = (1-5i)(1-z)⇒ z = 1 - z - 5i + 5iz⇒ (2 - 5i)z = 1-5i⇒ z = 1-5i2-5i

Q: (d) Let Z₁ = −4+ 8i and Z₂ = -1 -2i. Show that (i) 21/2₂ | = 4. | (ii) (iii) |z₁|² +Z₁ Z₂ = 100.…

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Q: Find the real solutions of the given equationt 3x³+8x = 2 – 3x

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Q: Solve in terms of BesseL function, The DE :0 y + xy - ²xy -2 then express The solution in terms of…

A: The given Differential equation is We have to solve the given differential equation in terms of…

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Q: Express cos { θ + π/2 ) and sin { θ + π/2 } ) in terms of cosθ and sinθ.

A: Given  cosθ+π2, sinθ+π2

Q: Find all the solutions in radians of the following equations sin x + 2 cos? x = 1

A: Answer

Q: Find all solutions to the quadratic equation for x in radians such that 0sx< 2T. 2 cos? x + cos x –…

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Q: 2 sin(x) – (-v3) = 0 List all solutions in [0, 27):

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Q: 9. (9x + 25) (13x-19)/(17y + 5)',

A: label the points as: A,B,C,D,E,F,G and H.