Q) use demovier's theorm to find the three cubes roots of the following number                  -4-5i Solve this question

Q: 1. Solve the following complex roots and plot the solutions if

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

Q: 12. Use Euler's formula to write each of the following complex numbers in the form a + bi. (a) emi/3…

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Q: Given that x = 1-4i is one root of the quartic equation 2-82' + 54z - 152z +425 = 0, find the other…

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

Q: Find the four fourth roots of -1 -√3 i.

A: Given, z=-1-3i

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

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Q: 4. Find the three complex cube roots of 8.

A: Consider the given number 8,

Q: Solve for a: 63I+7 _ 36219 T =-25 Or=-11 Or 16 O=25

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Q: I. Solve using De Moivre's Theorem. Find the 2 square roots of 3 – 8i

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Q: Solve the following equation using the quadratic formula. 2x2 = = -9x + 12 The solution set is (Type…

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Q: Find the cube root of unity using De-Moivre's theorem and apply the same theorem to find the square…

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Q: Which of the following is not a root of the cube root of 1? o 1 iv3 - 2 iv3 - - 2 2 1 iv3 - 2 2

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Q: Use the meaning of cube roots to find an exact solution to the equation v*+ 2 =' --2 without using a…

A: The given equation is . The solution can be found by cubing both sides.

Q: The 8th roots of a complex number would have arguments that differ from each other by ??? degrees.

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Q: Find the four roots of ( 3 + i4 )

A: We know that , Complex number is of the form , z = x + iy. Also , Polar form of complex number is…

Q: Need help on this question. Stuck

A: We write the complex number using polar form.

Q: Find the value of the real number a if -1 – 2i is a root of the equation z² + az +5 =0. What is the…

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Q: 9. Find the four complex fourth roots of unity and plot them. 10. Find the six complex sixth roots…

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Q: 2. Write the number (2 – i)(-1+3i)(3 – 4i) in the form of +bi .

A: The detailed solution is as follows below:

Q: Evaluate the cube root of z = 27 cis (240 degrees) . Then raise them to the cube.

A: According to the given information, it is required to evaluate the cube root of the given function.

Q: Find all the complex fifth roots of 243. Write roots in rectangular form. Zo = 3+0i (Type your…

A: Complex Number

Q: Find all the complex fifth roots of 243. Write roots in rectangular form. ..... Zo =U %3D (Type your…

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Q: Find all complex cube roots of – 4 – 2i. Give your answers in a + bi form, separated by commas.

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Q: The complex cube roots of 1+ V3 i.

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Q: The fifth roots of 1 are

A: We have to find the fifth root of 1. Let z=15 ⇒z5=1 We know that e2kπi=1 for every k∈Z. Hence,…

Q: Find all complex cube roots of – 4 + 3i. Give your answers in a + bi form, separated by commas.

A: We’ll answer the first question since the exact one wasn’tspecified. Please submit a new question…

Q: Use DeMoivre's theorem to find the three cube roots of the following number. - 4- 5j

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Q: Find FOUR FOUsth roots -1+ 9i

A: Given complex no. is - 1+9i = z-1+9i can be expnessed as . (-1)2 + (9)2 [180-tan-1(9)…

Q: Find all the complex fifth roots of 243. Write roots in rectangular form. Zo =U (Type your answer in…

A: follow next step

Q: Use DeMoivre's Theorem to find the cube roots of Give your final answers in rectangular form. -8j…

A: Consider the given complex number, z=-8j here the objective is to find the cube root of the given…

Q: To find the principle nth root of a complex number, find the nth root of the _________and divide the…

A: let z = r cos 'theta' + i . r sin 'theta', be a complex number. Then the nth root of z will be:…

Q: Q) use demovier's theorm to find the three cubes roots of the following number                =…

A: Let us first try to express given complex number in r,θ form i.e., rcosθ+isinθ -4-5i=-4+5i divide…

Q: Find the roots of (-i +1) all to the power 1/3

A: Our objective is to find the roots of (-i +1) all to the power 1/3

Q: 13. Find the 3 Cube roots of Z = 27i. Write your final answers in rectangular form

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Q: 5. Find the 3 3rd roots of -27i, and graph them in the complex plane.

A: -27i=27cos-π2+isin-π2 Now, use De Moivre's Formula

Q: I. Solve using De Moivre's Theorem. Find the 9th roots of 12 – 13i

A: Consider the provided question, According to the given information, it is required to find 9th roots…

Q: Find the 4 4th roots of 4+10i

A: Given: z = 4 + 10i

Q: B- The Modulus and Argument of a Complex Number Z is (8, 90°) respectively find Vz4

A: We will find out the required value.

Q: (4) Determine the roots in rectangular form, (-14 + 3i) 2/5 (Note: Sketch your answers in the Argand…

A: Given: -14+3i-25 To find: Roots of the given complex number and Sketch the Argand diagram.

Q: Find the imaginary component if the nth root of  a + bi is determined for a = 9, b = 3, and n = 6.…

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Q: d. Find the 3 third roots of 1 and show their geometrical representation.

A: Let the cube root of 1 is "a"13=aCubing on both sides we geta3=1 or a3-1=0we know that…

Q: Find the three cube roots of -27i.

A: Find the three cube roots of -27i. We can split the number as 3 * 3 * 3 * i * i * i Applying Cube…

Q: 4. Classify the solutions to the following equation using only the discriminant. Select one of the…

A: We have to classify the solution

Q: Find all of the complex third roots of i .

A: given complex number is i. we have to find all of the complex third roots.

Q: Find the two square roots of 36i.   3Ï2 + 3iÏ2, -3Ï2 - 3iÏ2

A: z=36i=0+36i Now, r=02+362=36 & θ=tan-1yx=tan-1360=tan-1∞=π2 Now the polar form is,…

Q: Find the indicated powers and roots, giving the results in algebraic form: 1) the cube roots of – 8…

A: The cube root of the expression – 8 + 8i is given as: -8+8i3

Q: According to Descartes's rule of sign, how many possible positive and negative roots are there for…

A: Answer is  3 positive roots  And 1 negative root. Explanation is given below..

Q: Use DeMoivre's theorem to find the three cube roots of the following number. - 4- 5j What are the…

A: First convert the complex number to the polar form, a+jb=rcosθ+jsinθWhere,r=a2+b2;θ=tan-1baHere,a=4;…

Roots

The main dissimilarity between real and complex roots is that the real roots are obtained as real numbers, in contrast with the complex roots, which are indicated as imaginary numbers. The standard format for depicting any complex number is in the form of a + bi.