Find each of the following in rectangular (a + bi) form if z = 2 – 3i; if z = x + iy. 1+z 23. 1- z

Q: r the following. Square roots of 36(cos 90° + i sin 90°) e + 360°k Vcos 9 + 360°k +i sin (a) Use the…

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Q: Given that the characteristic equation has the following roots , what is the complementary solution?…

A: Given are the roots of a characteristic equation    1±3i,1±3i⏟,  2,2,2,2,4⏟       Repeated…

Q: One of the following has only one nilpotent element Z[i] = {a + bi : a, b e Z}

A: Given problem is :

Q: Given that the characteristic equation has the following roots , what is the complementary solution?…

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Q: C. Express each of the following as a sum or difference of circular functions. 1.3cos 70 cos50…

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Q: Find the four fourth roots of  z = 81(cos 4pi/3 + i sin 4pi/3) w0=  w1= w2= w3= .  Write each…

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Q: 6. Z=2(cos12° +isin12°) Find z', and write in the form a+bi

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

Q: 1. Use trigonometric substitution to evaluate each of the following. (») /: dx x² + 4x + 3 (b) dx (4…

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Q: Find zw and . Write each answer in polar form and in exponential form. 2т z = COs 3 +i sin 27 and 57…

A: Given:z=cos2π3+isin2π3w=cos5π9+i sin5π9zw=?zw=?

Q: 4. Find the distinct roots of z for the following equation, z4 = 3i. %3D 5. Prove by taking z = a +…

A: Q4) Given that z4=3i So z4=3iz4=3cosπ2+isinπ2z4=3cos2nπ+π2+isin2nπ+π2         Since sin and cos are…

Q: Express in the form a + bi where a and b are real numbers.

A: To: Express in the form a + bi where a and b are real numbers 5(cosπ+i sinπ)

Q: 2. Write each of the functions in the form Aet cos Bt +iBed sin Bt, where a, B, A, and B are real…

A: To write each of the given function in the form  A* eatcos(bt)+Beat sin(bt) . We apply three…

Q: Given that z = 3(cos 60° + i sin 60°), then the following is true.

A: Given data is: z=3cos60∘+i sin60∘

Q: Given that the characteristic equation has the following roots, what is the complementary solution?…

A: We will find out the required complementary function.

Q: -T/2 Evaluate using Wallis' Formula: sins x cos6 x dx

A: Use Wallis formula.

Q: find the mclaurin seies for the folloeing a. sin(2x) b. 1/1+3x

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Q: Evaluate by Wallis's Formula. Show the complete solution. S cos 30 de

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Q: Find all values of u between 0 and 2π that satisfy the following equations.

A: given,        cosθ=1/2

Q: Find the four fourth roots of z = 256( cos 21 + i sin 3 Write each root in standard form. 3 Wo =…

A: The given question can be solved as shown in step2.

Q: Find the co perpendicular to the li

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Q: Simplify the following expressions and express in the form a + bi. (2cos () + 21 sin (9) (a) (1]

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

Q: Indicate the two quadrants e could terminate in if sin A (Select all that apply.) O quadrant I O…

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Q: Given that the characteristic equation has the following roots, what is the complementary solution?…

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Q: Exercise 3: Solve the following equation for x and y where 3 xy – 2i + x + 2xyi – 5 =- 3i | 2

A: This kind of problem we can solve by comparing the real and imaginary parts and after that solve the…

Q: = 0. AW yy - If w = (y – 2x)³ - Vy – 2x, show that wxx | %3D

A: Function is the unique relation where each x is mapped to unique y. It can be of many type,…

Q: 31. Refer to Figure 23(B). Compute cos y, sin , cot , and csc ự. 0.3 (A) (B)

A: Solution: Consider the given figure (B), hypotenuse= h = 1 base = b = 0.3 So, the perpendicular  = p…

Q: Using de Moivre's theorem to compute (−1−√3i)^11 we find that the answer is?

A: For any complex number x and any integer n, r ( cos ⁡ θ + i sin ⁡ θ )n = rn (cos ⁡ ( n θ ) + i sin ⁡…

Q: Find the following equations on the complex functions: 1)cosz=sinh7

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

Q: Write the following with trigonometric form : 1) z = -V6 - V2i 2) z = -3i 3) z = 3 + 4i 4) z = -2 +…

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Q: that is an ei -1

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Q: Find the four fourth roots of z = 16( cos + i sin 3 Write each root in standard form. Wo = W1 = W2 =…

A: We will use the De-Moivre's theorem to find out the 4th roots of the complex number.

Q: Solve the given differen hal equat.or by unde termined coeFFICients ay= (x-9) sin ?

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Q: Given that z= Inx2+y? +tan- then the value of will be ax? ay

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Q: Find u to the nearest tenth of a degree if 0 <= u < 360°,        cos u = 0.2351

A: cos u = 0.2351 cos is positive in first and fourth quadrant. So if x is the angle in first quadrant,…

Q: Sketch the following signals: 1.1.1 xn]=2 sin(32). 1.1.2 xn] = 4 cos(m – 2). TTn

A: The signal is xn=2sin3n. For each n, sketch as follows:

Q: If y = y(t), write y' in Leibniz notation. %3D Enter the answer in the box.

A: Question is based on Leibniz notation.

Q: Write each of the following complex mumbers in the exponential form. (a) i cos (c) 1-1/3 584

A: We know that,z=rcosθ+isinθAnd, eiθ=cosθ+isinθTherefore, z=reiθ

Q: Given that the characteristic equation has the following roots , what is the complementary solution?…

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Q: eax cos bx dx

A: Use integration by parts

Q: Given the following equations and graphs: Y1 = a1 sin(b1z) Y2 = a2 cos(b2z) where b and b2 are both…

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Q: Find the exact value of each of the Following under the given condihons. 3T, tan a = TLAL and cos B…

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Q: Find all values of A E C such that A(1+2i, 5+4i) = (3+2i, 6-1)

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Q: 1. Express in the forrm a + bi. a) (1+ 3i)(1 – i) b) (-3+ i)/(7 – 3i)

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Q: Solve the following Bernoulli equation 3 ux %3D

A: 1.  We solve the given differential equation by substitution and then separating the variables. 2.…

Q: Find sin zj and cos ( – nj) in the form u + jv.

A: Brief answer is given below.

Q: Given that the characteristic equation has the following roots, what is the complementary solution?…

A: We have to find the characteristic equation.

Q: 12. Find another representation, (r, &theta), for the point under the given conditions. 1, and 2n…

A: We know that the angle around a point is 2pi. Hence pi/3 = 2pi+ pi/3

Q: Eliminate the parameter t from the following: x= 9 sin t, y = 9 cos t

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Q: Find the four fourth roots of z = 256(cos4pi/3 + i sin4pi/3)    w0= w1= w2= w3=

A: Solution...

Q: Given that the characteristic equation has the following complementary solution, what are its roots?…

A: The given complementary solution is y=(c1+c2x)cos2x+(c3+c4x)sin2x