Use De Moivre's theorem to solve for z given z = 3 – 2i. Write your answers in rectangular form. Use at least 3 decimal places in your final answer where necessary.

Q: Find the three cube roots of -8i.

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Q: Find the k=8 root of the 10th root of 1+i. Express the answer in rectangular form in 4 decimal…

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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: Find the two square roots of i.

A: Let's assume  i=a+ib                                                          ..1 Where, i=-1

Q: Find all 4 roots of the equation z4+1=0.

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Q: Find the real component if the nth root of a + bi is determined for a = 10, b = 8, and n = 5. Round…

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Q: Does the equation 3.2x° – 53.4x = 0.015x – 43 have any root that is not an algebraic number? Justify…

A: Given that 3.2x6-53.4x=0.015x3-43 The equation can be written as, 3.2x6 -53.4x=0.015x3-433.2x6…

Q: Find (root3 / 2 - 1/2i)30 by the de moiver's formula.

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Q: Find the roots of z = v5 – 6i %3D -

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Q: Find all distinct roots (real or complex) of z²+(−5+3i)z+(10–10i). Enter the roots as a comma-…

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Q: -1 2x -бу -3 3 -1 -8y U Xu Use only positive exponents in your answer.

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Q: If w =-i, determine all the roots of Vw. 2

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Q: Find the real component if the

A: Given,             a+bi Here,         a=9,  b=10, and n=7.

Q: Find all the values for the fifth root of z = 32

A: We have to find all the values for the fifth root of z=32.

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: Find the imaginary component if the nth root of a + bi is determined for a = 10, b = 8, and n = 7.…

A: Imaginary component of the function

Q: Find the rectangular forms of all 6th roots of z = -6

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Q: Determine the four roots of z = -2 + 2i.

A: Given: z=-2+2i To find the four roots of the given complex number. The complex number into polar…

Q: Perform the indicated operations and express your final answer in exponential form: 2i* – 3i + 5i?…

A: The complex number, z=x+iy can be written in the exponential form as z=reiθ , where, r=x2+y2 and…