Find the indicated power using De Moivre's Theorem. (Express your fully simplified answer in the form a + bi. 12 2.

Q: (b) Show that i10 is real, even though i or 10i is not.

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Q: Prove the Euler's formula: e" = cos0+ jsin 0 using the definition of the complex number

A: We have to prove that ejθ=cosθ+jsinθ. We know that ex=1+x+x22!+x33!+x44!+.......... Now,…

Q: 5(2-3i) – 4(4+6i)

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Q: A = 2i+3j+5k and B = 3i+6k, Determine the direct cosine of (AXB). %3D %3D

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Q: (a) Use the formula zk = Vr(co e+ 27tk cos +i sin 0+277K to find the indicated roots of the complex…

A: Given Z=-322(-1+i) Zk=rncosθ+2πkn+sinθ+2πkn, 0≤θ<2π The trigonometric form of the complex number…

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

A: Complex number a+ib form

Q: Use De Moivre's Theorem to evaluate [-6+ 2i]6

A: Any complex number z=x+iy can be represented as  z=r(cos θ+isin θ) , where r=x2+y2, θ=tan-1 yx.  De…

Q: Find the indicated power using De Moivre's Theorem. Leave the answer in a + bị. 6.

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Q: 5. e-1+4i 5. cosh(2e3')

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Q: A number of the form iy is called pure imaginary ylgn İhi

A: True

Q: a) Find the square root 14+ 4√6. b) If ƒ(r) = (2+1), show that ƒ(r) — ƒ(r+1) = r(r+1}(r+2). Hence,…

A: B. f(r) - f(r+1)

Q: If Zo is any complex number interior to any simple closed contour prove that dz 2πί, η- 1 Jc (z-…

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Q: Let z be a complex number with |z = 11 and let z0 = 17 – 20i. What is |z – z0| + |z+ zo|??

A: Given:- Let z be complex number with |z| =11 and z0 =17 -20i  To find:- value of |z - z0 |2 +  |z…

Q: Find w =a +bi , where a and b are real numbers. %3D 120-22i

A: Given120-22i

Q: Find the rectangular form of 3/2 et* i.e. the a + bi form.

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Q: Express in the form a + bi where a and b are real numbers.

A: To: Express in the form a + bi where a and b are real numbers 5(cosπ+i sinπ)

Q: 3. Use DeMoivre's Theorem to find the indicated power. Write the result in rectangular form a + bi.…

A: Consider the given expression. 4+i433 Let's the given complex number is z=4+i43. The form of the…

Q: Perform the indicated operations (answers in a + bi form): 3 + 4i / 3 – 4i

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Q: Express in the form a + bi, where a and b are real numbers.

A: 20cos11π6+ i sin11π6

Q: Given any two functions f(z) and g(z) and any complex number z0, is it always the case that…

A: Given any two functions f(z) and g(z).

Q: Find all the nth roots of z. Express answers in polar form z = 4 + 4i √3 , n = 3

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Q: 8) Use DeMoivre's Theorem to compute the three cube roots of v3+j. Write your answers both in polar…

A: First, let us compare the given complex number to the standard form of z=x+j y as shown below. x=3…

Q: Use de Moivre's Theorem to find the following. Write your answer in standard form. (−2√3+2i)4

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Q: Let z be a complex number. Then sinh(2z)-i is bounded in C.* False True

A: Given a statement

Q: V3 1 (- 2

A: given(-32-12i)20 =(-1)20(32+12i)20 =(cos30+isin30)20 The formula of Demoivre's theorem is cos θ+isin…

Q: To convert a complex number z = x + yi from standard form into trigono metricform, use the…

A: The modulus of a complex number z=x+yi is r=x2+y2 & the amplitude or argument is,…

Q: Sketch each of the following sets of complex numbers z that satisfy the given equations/inequalities…

A: We will use basic Complex analysis

Q: Find w a + bi = z, where a and b are real numbers. %3D 60i-11

A: We have the formula x+iy=x2+y214costan-1xy2+isintan-1xy2

Q: 4. This question has two parts. a) Compute the value of eln 2020+3xi/4 b) Find all complex numbers z…

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Q: Let z = -4 + 3i and zw = -7- 2i. By showing clear steps, find w in the form of a+bi.

A: Given  z=−4+3izw=−7−2i

Q: 5) A = 2i+3j+5k and B = 3i+6k, Determine the direct cosine of (AXB). %3D %3D

A: Finding the cross product of vector A and vector B  i×i=j×j=k×k=0, i×j=k, j×k=i, k×i=j, j×i=-k,…

Q: Write the following with trigonometric form : 1) z = -V6 - V2i 2) z = -3i 3) z = 3 + 4i 4) z = -2 +…

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Q: Find the indicated power using De Moivre's Theorem. (Express your fully simplified answer in the…

A: Let z = 1-iFirst write z in polar formr = sqrt((1)2 + (-1)2) = sqrt(2) = tan-1(-1/1) =…

Q: If Zo is any complex number interior to any simple closed contour C prove that dz 2πί, η -1 c…

A: Let C be a simple closed contour and let z0 be a complex number inside C. Prove that:…

Q: Find the indicated power using De Moivre's Theorem. (Express your fully simplified answer in the…

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Q: it is given that z+2i=iz+A, w/z=2+2i, Imw=8, where z and w are complex numbers and A is a re…

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Q: 6. Use DeMoivre's Theorem to calculate (–/3 + i) Write your answer in a + bi form.

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Q: Solve for z, and give your answer in the form a+bi. z/(5+4i+z) = 4-5i %3D z = 0

A: Given  The equation is z5+4i+z=4-5i

Q: Use De Moivre’s theorem to change the given complex number to the form a + bi, where a and b are…

A: Given: The complex number -32-12i50.

Q: Use De Moivre’s theorem to change the given complex number to the form a + bi, where a and b are…

A: Solution: Consider the given complex number is: z = 3 + i7 We have  z = a + ib⇒z = rcos θ + i sin θ…

Q: If Z is complex number e? = e*(cos y + isin y) True O False

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Q: Find the distance d between z1 = (-7– 6i) and 22 = (-15 – 12i). %3D

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Q: Ifz is a complex number, then sin-z can be written as (A)-i In iz+ (1-z) (B)t In [iz + (1 -z)]…

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Q: Use De Moivre’s theorem to change the given complex number to the form a + bi, where a and b are…

A: Given complex number is: 22+22i25 Let us consider, r cos θ=22r sin θ=22 Then we get,…

Q: A. Find the indicated power using De Moivre's Theorem. Leave the answer in the form a + bi. 6. +

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Q: Let z be a complex number. Then sinh(2z)-i is bounded in C. * False True

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Q: c) By using De Moivre's theorem, find (3/5 – 3i) in the standard form.

A: To find complex no. in standard form using De Moivre's theorem .

Q: Use De Moivre's theorem to simplify the expression.  Write the answer in a+bi form: (1+i)20

A: To use De'moivere theorem first we have to convert the given complex number into place form then use…