Use DeMoivre's Theorem to determine the following power of a complex number. Write the answer in form a + bi, where a and b are real numbers and do not involve the use of a trigonometric function. (* - 4) - 5 V2

Q: Recall Yung's last step before requiring assistance: 6± √36-40 x = 2 Yung knows that 36-40 is a…

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Q: Show that the roots of px2 + (p - q)x - q = 0 are real for all real values of p and q.

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Q: Explain how the Pythagorean Theorem can be used in the real world. Who might use it on a regular…

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Q: Example 2.41. Find all roots of the equation x³ - 2x² - 5x+6=0 by Graeffe's methoc squaring thrice.

A: Please find step by step solution below:

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A: Since the roots of the given equation are real and distinct, We must have…

Q: What does Descartes’ Rule of Signs tell you about the real roots of x3 – x2 + 1 = 0 ?

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Q: is the quadratic formula an identity

A: The objective of this question is to determine whether the quadratic formula is an identity.

Q: If r; and r, are the roots of equation x² – 2x+4 =0, then find Er .

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Q: (b) The quadratic equation x² + px + q = 0 in which the coefficients p and q are real, has a complex…

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Q: Form a quadratic with real coefficients having amongst its roots -6+i

A: As given in this question, one root is imaginary then other will also be an imaginary roots.

Q: х? - 2 8х + 65 — 0

A: we use i = √-1 and Quadratic formula

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Q: Prove that there are no integer solutions to the equation x² = 4y + 3

A: To prove that there are no integer solutions to the equation…

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: In the quadratic equation Ax²+BX+C =0' describe the roots when B2-4AC is positive. O The roots are…

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Q: If the roots of ax² + bx - 2 = 0 are a + b = 1+√3 3 I what is a+b?

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Q: Find ||v||. v= - 4i + 7j - 2k v = (Type an exact answer, using radicals as needed.)

A: topic - magnitude of vectors

Q: Use DeMoivre’s theorem to find the cube roots of 8 (i.e. let’s solve the equation z3 = 8 for z).

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Q: Give your answer in a +bi form

A: Calculate 4+2i and give your answer in a+bi form.

Q: Find all solutions (real and complex) z in Cartesian form (a+bi) to the equation rº –9r+8 = 0.

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Q: Prove that there are no integer solutions to the equation x2 = 4y + 3

A: Given equation:- x²=4y+3  We have to prove that the given equation don't satisfy integer pair of x…

Q: (b) a, 3 andy are the roots of the equation 2x³ + 5x² - 4x + 8 = 0. Given that a ² +8² -341 8 find…

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