Find the three cube roots r1, r2 and r3 of 8(cos 264° + j sin 264°). Express all arguments in degrees in the form (r, 0) where r is the absolute value of the root and e is the corresponding argument in degrees. r2 =-

Q: (b) Show that i10 is real, even though i or 10i is not.

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A: We will use long division to factor the four degree polynomial into the product of two quadratic…

Q: m = -3, -2+i,

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A: The given complex number is: z=-1-3i Formula: The n-th root of a complex number z=rcos θ+i sin θ is…

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A: We have the formula for rational root of complex number

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A: Given  z=16cos60°+isin60° To find the fourth root De Moivre's theorem for finding complex root is…

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Q: Consider the following. Cube roots of -343 0 + 2xk 0 + 2rk (a) Use the formula z = V7(cos + i sin to…

A: The detailed solution is as follows below:

Q: Solve for 0 if-4sin 0 + 6 = 2 and 0 <0 < 2n. List your answers as exact answers in terms of t,…

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Q: Solve for z, and give your answer in the form atbi. 2z+z =-5+i+2-2i z = 0

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Q: If 7, r, and r, are the roots of equation x-2x+3=0, then findErr,. إختر أحد الخيارات: -2 a O .b O…

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Q: Consider the following. Cube roots of -32V2(-1 + ) (a) Use the formula z = V7(cos 0 + 2xk 0 + 2xk +…

A: We first write -322(-1+i)=322-322i in the polar…

Q: Identify the roots of the DE from its auxiliary equation: у" - - бу %3D 0 бу" + 11у' — Select one:…

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Q: Find all the real roots of p(r) = 3z + 3r – 108z – 108 %3D | given that -1 is one of them.

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Q: Find all the third roots of i

A: the solution follows as

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A: In this equation, two integers and their squares are added on the LHS. Squares of integers are…

Q: Find all the roots of z = -4 + (4V3)i giving each root in the form re". %3D 8° = -4+ (43) C

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Q: Solve for z, and give your answer in the form a+bi. z+3z = 5-3i+(-25–5i) z = 0

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Q: 59. Let a, c +0. Show that the roots of ax? + bx +c = 0 cx? + bx + a =0 and are reciprocals of each…

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Q: Find FOur Fousth Roots of -1+2i

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Q: obtain the four roots of characteristic equation as follows: p+ Vp? – 8pi? 272 p- Vp? - 8pi? 212 12…

A: As per the instruction, we will have to find the roots that are marked in blue. So, we will be…

Q: Find w a + bi = z, where a and b are real numbers. %3D 60i-11

A: We have the formula x+iy=x2+y214costan-1xy2+isintan-1xy2

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A: Solve the following

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A: To determine: The value of u, where u is a real number, 4√u = 2

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A: The representation of a complex number can be done in two forms, rectangular and polar forms. The…

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Q: Calculate the discriminant and determine the resulting number of solutions. 4x - x2 = 17 %3D BIUE E

A: We have to find

Q: Find all distinct roots of z* +3-3i = 0 and write them in  the form x+iy.

A: z*= x - iy

Q: B. Find the indicated powers and roots, giving the results in algebraic f 1. [2(cos1500 +isin…

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Q: Find all solutions of the equation in the interval [0, 2?). (Enter your answers as a comma-separated…

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Q: Solve the equation on the interval 0 s < 2л. tan(20) = -1 %3D 3T 7n 11T 157 8. 8 8

A: Here we have to solve the equation, tan(2θ)=-1 on the interval 0≤θ≤2π.

Q: Find the two roots of (5 + /3)/2 in rectangular. a) 2.327 + j0.6446, –2.327 – j0.6446 b) -2.327 +…

A: Given complex number is 5+j3. Write this in polar form. Then, r=52+32=36=6 θ=tan-135 Hence the polar…

Q: csc² () - - 2cot 2cot ) = || .2

A: Given, The trigonometric equation  csc2(x/2)-2cot(x/2) = 0 We have to find all solution in the…

Q: Find w a +bi = Jz, where a and b are real numbers. -60i-11

A: Given, w=a+ib=z -60i-11

Q: Find w a + bi = Jz, where a and b are real numbers. %3D -15+8i W%3=

A: Given: -15+8i And, w=a+bi=z

Q: Find the three roots of (-6 + 4i)'/3 Enter these in order of increasing angle, going from ) = ()…

A: Firstly find the tangent of angle using the below formula. If z=a+ib the acute angle θis…

Q: Calculate the value of (1+2i)? and then use this value to find the roots of z- z+ (1 – i) = 0. (1+…

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Q: Find all solutions of the equation and express them in the form a + bi.

A: Given: 70. t+3+3t=0

Q: answers in terms of i,j and k.

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Q: Solve for z, and give your answer in the form a+bi. z=(-5+31)(-5-4i+z)

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Q: 2. Use the quadratic formula to find the roots of the equation: 5x - 4x +8 = 0. -4+ 12i 5. O x = 3…

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Q: Find the three cube roots of  z= -2 + i

A: Given The given complex number is z=-2+i. Use De Moivre's theorem for nth root of complex number…

Q: (b) Show that ii is real, even though i or 5i is not.

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