Use DeMoivre's Theorem to find the following. Write your answer in standard form. (1 + 3) - 16/3 + 16i 64 - 8 O - 8+8iy3 - 8- 8iy3

Q: Express the following in the form a + bi, where a and b are real numbers: 3-4i

A: Explanation; Given that: Concept: Make a perfect square.

Q: Express in terms of i. V- 121 V- 121 %3D (Simplify your answer. Type your answer in the form a +…

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Q: Determine the three roots of -32/2 - j32/2-32 2 - j322 .

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Q: for what value Of real nunber? b will the product below be a (a-3i)(6+bi)

A: The given expression is: (2-3i)(4+bi)

Q: Write a in the form a = a-T+anN at the given value of t without finding T and N. r(t) = (3t + 4)i +…

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Q: Let u = 7i - 9j, and w = -i-7j. Find ||w- u||. ||w-u|| =O (Type an exact answer, using radicals as…

A: Topic - vectors

Q: Write a in the form a = a7T+anN at the given value of t without finding T and N. r(t) = (- 2t + 3)i…

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Q: Find all the solutions to the polynomial: x* + 4x°+7x² + 16x + 12 = 0 1 -4 -2i O 2i -3 O -1

A: A polynomial function is a function that involves only non-negative integer powers or only positive…

Q: IF A= 3i-2j find A.A *

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Q: Solve the following quadratic equati ons by factorization x+3 1-x 17 (ii) X-2

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Q: Evaluate the sum or difference, and write the result in the form a + bi. (-4 + i) - (2 - 5i)

A: To evaluate the difference

Q: 18. Simplify: i9 + j21 + j2050 in form a + bi.

A: Complex number a+ib form

Q: Find all the real square roots of 0.0004. 0.00632 and -0.00632 0.06325 and-0.06325 0.0002 and…

A: The square root of 0.0004 can be determined using the general method.   Write 0.0004 in the general…

Q: Determine all the roots of z +1 = 0

A: The given question is related with complex analysis. We have to determine all the roots of z4 + 1 =…

Q: Find x so that the distance between (−2, 6) and (x, 4) is square root of 29. .  (Enter your answers…

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Q: Use DeMoivre's Theorem to find the following. Write your answer in standard form. (- 4+41) 128+128i…

A: The solution is:

Q: 6. Find all tu roots for each espression. (a) (-2+ 2i) (b) (-3) (c) (2i)

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

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Q: Find the sum and product of the roots. 1.) x2 + x - 20 = 0

A: topic - sum and product of roots

Q: 5) Evaluate and write the result in the form a + bi. ə) (-) 2+i b) 2-3i

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Q: Evaluate the product, and write the result in the form a + bi. (2 + 5i)(2 - 5i)

A: The given expression is (2 + 5i)(2 - 5i)

Q: Find the roots. z^2 =1−2i z^4 =−2−5i

A: For solving an equation of the form z2=a+ib, where a+ibis known, we assume that z=x+iy to  get that…

Q: Express the following in the form a + bi, where a and b are real numbers: 60i-11

A: Introduction: Like a real number, the square roots of a complex number can also be determined. A…

Q: One of the roots of x^4 + 9x^3 + 48x^2 + 78x –136 = 0 is -3+5i. Find the other three roots. Using…

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Q: Express z =1/(2+5i) in the form a+ib.

A: Given:

Q: Use DeMoivre's Theorem to find the following. Write your answer in standard form. -8 – 8i3 8+8i -16…

A: Explanation of the answer is as follows

Q: The roots of (x + 1)2 + 1 = 0 are

A: NOTE: Refresh your page if you can't see any equations. . subtract 1 from both sides

Q: Do not use a calculator in this question. Find the positive value of x for which (4 + V5)x² + (2 –…

A: 3 Given equation is 4+5x2+2−5x−1=0. We have to find the positive value of x. The solution of the…

Q: Let u = 5i - 7j, and w= -i-4j. Find w-u|. w-u = (Type an exact answer, using radicals as needed.)

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Q: Find the distance between the two points in simplest radical form. 10 9. 7. 6. 4 3 10 9 -8 -7 "5 4…

A: Given: The objective is to find the distance between the two points.

Q: Perform the computations in the given question and express the results in standard form a+ bi.   (2…

A: Given: 2-3i-1+4i Simplify the expression: 2-3i-1+4i=2-1+4i-3i-1+4i=-2+8i+3i-12i2=-2+11i-12i2

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

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Q: Use de Moivre's formula to evaluate (-2 + 2i)1º. Express your answer in standard form or, in a + bi…

A: De Moivre's Formula: For any positive integer n and complex number x=a+ib, the de Moivre's formula…

Q: 15. Find the two square roots of the following and write your answer in standard form. 2+ 2iv3

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Q: (b) Show that it is real, even though i or 8i is not.

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Q: Let p(x)-x-5x?+4x-20. Verify that p(5)-0 and find the other roots of p(x)-D0.

A: p(x)= x3 - 5 x2 + 4x -20   Verify that p(5)=0; p(5)= 53- 5*52+4(5)-20 p(5)=0   Hence, x= 5 is one…

Q: Evaluate the product, and write the result in the form a + bi. 4(-1 + 2i)

A: To evaluate the product: 4(-1+2i). Solution: 4(-1+2i) On simplifying further we get:…

Q: Write a in the form a = a-T+ anN at the given value of t without finding T and N. r(t) = (2t + 3)i +…

A: see below the answer

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

A: z*= x - iy

Q: Use Steffensen's method to find, to an accuracy of 10-6, the root of x −2¯* =0 that lies in [0, 1].

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Q: Express in the form a + ib where a and b are real numbers. V1 - 2i

A: We will find out the required value.

Q: Evaluate (V12 - V-3) (3+ v-4) and express in the form a + bi, for SOme rea numbers a and b.

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Q: Find the sum and product of the roots. 1.) x2 + 8x + 15 = 0

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

A: Here we use DMoivas rule.

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

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Q: Q3/ by using De Moivre's theorem find the third roots of 23 – 1 = iV3

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Q: Solve the following equation for x. Let X= 2*. 2* - 40• 2 +256 = 0 X3= (Use a comma to separate…

A: Properties of exponent: 1) if am = an then m=n.

Q: Find the sum and product of the roots. 1.) x2 - 6x + 18 = 0

A: we have  to determine the sum and product of the roots