(a) Make use of De Moivre's Theorem to calculate (3√3+3i)5 and leave your answer in the form a + ib. (b) Find the cube roots of -2 + 2i and leave your answers in polar form.

Q: Solve the following complex number problems: a. Simplify: i5 + 3i35 + 2i23 – 2i12 (5+31) (3-41) b.…

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Q: (a) Integrate the following functions with respect to x: (i) 3x2 + 5x -7 (ii) x +

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Q: Find the 3 complex numbers z E C that satisfy the equation z³ = -27. Write the solutions in polar…

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Q: a) Calculate z= 3√3 as a complex number in cartesian representation. 2-√3i b) Rewrite your result as…

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Q: Form the differential equation for the function y = ae3x + be-3x O a. y" +2(y)2 = 9y? O b. 2yy" -…

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Q: 1. Solve the following complex number problems: a. Simplify: i55 + 3i35 + 2i23 – 2i1² (5+31)(3–41)…

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Q: with r > 0 and

A: WE HAVE FIND THE POLAR FORM OF THE QUESTION. HERE I AM PROVIDING MY HANDWRITTEN SOLUTION

Q: 3. Evaluate the following complex number a. (30460° +20<-20°) b. 302-30° +(4-j3)(3+j4)(4-j5)* C.…

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Q: a) Calculate. 2= 8i √3-i as a complex number in cartesian representation.

A: (a) To Calculate:  z=8i3-i as a complex number in cartesian representation.             Note: As…

Q: Solve the equation and sketch the solutions in the complex plane  z5 = -16√3 + 16i

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Q: For the complex number z = 3 – 4i, solve for z2 – 12z + 52.

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Q: a) Calculate these complex numbers and express the results in rectangular form. 322-20° +…

A: Calculate the complex number and express the results in rectangular form .

Q: I. Solve for the negative of the following complex numbers. a.z = 2- j8 b.-z = -3 + j45 C.z = 67 -…

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Q: Express the complex number z = 9√3+9i in standard polar form.

A: The given complex number,    z=93+9i

Q: 3. Success! You have saved Mr. Henville from the burning tower! Now you must get him safely back to…

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Q: V3 (b) Write the complex number (-+603 in the simplest form 2 (c) Let C be the arc of the circle Izl…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Let z, and z2 be two complex roots of the equation z2 + az + b = 0. Assume that the Origin, z1, and…

A: Given  Let z₁ and z₂ be two complex roots of the equation                  z² + az + b = 0. Assume…

Q: Find all the fifth roots of 1 + i√3

A: That's easy.

Q: Q. z =2+5i

A: Given complex number

Q: (4230°)-(2/225°) d. (24140°)(3/300°) (Express your answer in polar form)

A: The given problem is to simplify and express the given complex expression in terms of polar form.

Q: In((5+j3) + (6e12)] - 10430°

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Q: 1+ √3i 1+i 10

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Q: Express the result of each of these complex numbers manipulations in polar form.

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Q: Solve the following equation in the complex number system. Express solutions in both polar and…

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Q: From the following rectangular complex number Z-4+3i, Z-2-3i and Z,--5+2i Find the poler form?

A: Given:     z1=4+3i      z2=2-3i      z3=-5+2i For a complex number z, expressed in Cartesian form as…

Q: This question concerns the complex numbers, z, = 1 – V3i and z2 = C + Ci. (a) Plot the numbers z,…

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Q: b. (5+31)(3-41) (Express your answer in exponential form) 1+i С. Express your answer in item b to…

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Q: - find polar form of the complex number z = (2√3-4i) + (-√3+51)..

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