Use the half-angle formulas to determine the exact values of the sine, cosine, and tangent of the angle. π/8 sin П Cos T tan 8 800 = = 11 √2-1 2√2 √2 +1 2√2 √2-1 √2 +1

Q: how about complex number solutions?

A: Apologies for the inconvenience. One solution is x=-1, other 5 solutions we will get from x5=-32.

Q: Simplify the complex number i .45 as much as possible.

A: See solution below

Q: What we want to do next is to write a procedure to raise any complex number to any integer power (x…

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Q: Find two positive real numbers such that they add to 40 and their product is as large as possible.

A: Our Aim is to find two positive real numbers a and b such that they add to 40 and their product is…

Q: Find the three cube roots of 1.

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Q: Find the cube root of Z^3=8i lying in the first quadrant of the complex plan

A: Find the cube root of Z^3=8i lying in the first quadrant of the complex plane.  To find the cubic…

Q: Write the following complex numbers in exponential form. The principal value of ал the argument…

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Q: In the graph, 1 and 2 are complex numbers represented as vectors from the origin. What is 2-1? 4 Z1…

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Q: Find the roots, including the complex ones, of 2x³– 3x? = 1 using Newton's method.

A: To find the roots using Newton's method, 2x3-3x2=12x3-3x2-1=0Let, f(x)=2x3-3x2-1…

Q: Use DeMoivre’s Theorem to find all the cube roots of 2i. Show your work.

A: From the given z=0+2i. That is, a=1 and b=2. Recall the DeMoivre’s Theorem: "If Z=rcosθ+isinθ, then…

Q: Find the indicated roots and graph them in a complex plane URGENT PLEASE

A: First we have to convert given complex number into polar form-

Q: Suppose z is a complex number that possesses a fourth root w that is neither real nor pure…

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Q: 60 6-V-8 5. 6. 4 + V-25 -2

A: We have to simplify the complex numbers. 4. i460 5. 6--8-2 6. 4+-25

Q: Simplify the following expression to i, 1, -i, or -1. ¡64 64 =

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Q: Find all complex number solutions 3/ t-5 - 4t/t+5 = 56/ t2- 25

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Q: Find one of the roots of 2x3 +3x2 – 23x – 12

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Q: Use the Newton's method to find the real roots of 3x³+4x²8x - 2 = 0

A: Given:The given equation is .To Find:We have to find the real root of the given equation by using…

Q: Find the four roots of the number 16- as a result of the assumption

A: To find fourth root of 16 by asumption. Let x=164

Q: Show that all roots of Jnx are real.

A: Given: To show that all roots of Jnx are real;

Q: Find all of the roots of Vi.

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Q: Find real numbers a andb such that the equation is true. a+ bi = 11 + 7/ %3D

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Q: Ex : find the real part of analytic complex variable if imaginary part of it is v = (xy) V%3D

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