Q/ State and Prove the integral formula for the derivati ves Complex number

Q: Let z be a complex number. Then sin(3z)-i is bounded in C. * True False

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Q: Let z be a complex number. Then sin(3z)-i is bounded in C. * False True

A: See solution below

Q: Find a complex number z such that |sin(z)| > 1.

A: The objective is to find a complex number z such that |sin z|>1.

Q: If zisa complex number satisfying |z-1=1. z-2 Then provethat-i tan{arg (z)}

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Q: 1. Express the sum of (2 - 3i) and (6 + 4i) divided by the sum of (4 + i) and (-5- 2i) in a + bi…

A: 1)  To find the value of           {(2-3i)+(6+4i)} / {(4+i)+(-5-2i)}

Q: complex cube roots of -1 are and and hence prove tha 2 1+v? + v3i - V3i = 2 2

A: We have 1+3i23=-11-3i23=-1

Q: solve the complex number using De Moivre's Theorem 483 ( - V3 2

A: The general form of a complex number is given by z=a+ib, where a,b are two real numbers and i=-1.…

Q: using De-Moivre's theorem prove that cos π/7, cos 3π/7 and cos 5π/7 are the roots of 8x3-4x2-4x+1=0.…

A: The given equation 8x3-4x2-4x+1=0 Roots of the equation are cosπ7, cos3π7, cos5π7 use trigonometric…

Q: Find the modulus and principal argument of the complex number 4 -V5 + V5i 2/3 + 2i Give your answers…

A: Given the complex number is z=-5+5i23+2i4

Q: Let z be a complex number. Then the solution(s) of sinhz+coshz=1/e is (are) O z=2nti-1 where n is an…

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

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Q: Convert the rectangular form of the complex number 2 – 2i into polar form. Show all work and label…

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Q: Let z be a complex number. Then the solution(s) of sinhz+coshz=1/e is (are) z=2nti-1 where n is an…

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Q: (4) Prove the formula cosh x - sinh2 x 1 using the methods in this workshop. In other words, express…

A: Consider the given identity

Q: snip

A: A complex number can be written in the cartesian form a+bi and the equivalent polar form reiθ. Polar…

Q: 67 V3 1 Use De Moivre's Theorem to express the complex number on the form a+ bi. ---1

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Q: a) Show that the modulus of sum or difference of two complex numbers is always less than or equal to…

A: Use the properties of complex numbers to solve this problem as in next.

Q: Let z be a complex number. Then coth(2+7ti) is equal to cothz -cothz tanhz None of these -tanhz

A: Solution

Q: Let z be a complex number. Then sin (3z) -i is bounded in C . TRUE OR FALSE

A: It is an application of Linville's theorem

Q: Let z be a complex number. Then coth(2+Ti) is equal to -tanhz O None of these O -cothz O cothz O…

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Q: Find the cube roots of the complex number z = 125 (cos(60°) + i sin(60°)). Select all correct…

A: We have to find cube root of given complex number.

Q: Find the modulus of the given complex number. Give exact answers only and show your work. -7 - 5i

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Q: Let z be a complex number. Then tanh(z+Ti) is equal to * cothz -tanhz None of these tanhz -cothz

A: We know that hyperbolic identities

Q: Let z be a complex number. Then coth(2+m) is equal to * Ocothz O cothz O None of these tanhz, O…

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Q: Let z be a complex number. Then coth(z+JTi) is equal to -tanhz O None of these tanhz cothz -cothz

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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: Let z be a complex number. Then the solution(s) of sinhz+coshz=1/e is (are) * z=nti-1 where n is an…

A: This is a problem of complex analysis.

Q: Let z=x+iy be a complex number such that coshz #0. Then Re(tanhz) is equal to

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Q: Multiply. Leave Answers in trigonametric form. 21=1+1, 22=-3-3i %3D

A: Given complex numbers are z1=1+i,z2=-3-3i. Multiply the above numbers as follows.…

Q: Find a complex number z such that |sinz|>1

A: We have to find a complex number z such that |sin z|>1.

Q: i) Find real and imaginary part of complex number (V3 + i)° by using De Moivre's Theorem.

A: Consider the complex number: 3+i3 Comparing the complex number 3+i with standard form of complex…

Q: 13 Jlgull If z,,z, are two complex numbers then:

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Q: 1. nRoots of complex numbers 1. Find the 3roots of z1 = -V3 - iv2.

A: Given complex number is z1=-3-i2 Since we know that nth root of complex number is…

Q: 9. i) Express each of the complex numbers Z (2+3i)(1- 2i), Z2 = (3+ 5i)/2 - i in the form a + ib…

A: “Since you have asked multiple questions in a single request, we will be answering only the 1st…

Q: Let z be a complex number. Then tanh(2+JTi) is equal to cothz -cothz None of these -tanhz O tanhz O…

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Q: Let z be a complex number. Then the solution(s) of sinhz+coshz-e is (are)* None of these z=nti+1…

A: See solution below

Q: Let z=x+iy be a complex number such that coshz#0. Then Im(tanhz) is equal to

A: None of these is correct.

Q: Find all solutions of 2sin(x+1)=–√2 on the interval [6π,8π]. (Leave your answers in exact form and…

A: Solving the eqution

Q: Let z be a complex number. Then coth(2+Ti) s equal to * ● -tanhz O None of these ) -cothz O cothz O…

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Q: Let z be a complex number. Then sin(3z)-i is bounded in C. False True

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Q: Use Bombelli's approach to find a complex number c = a + bi such that = 18 + 26i where a and b are…

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Q: i Given two complex numbers zı = -6 – 3i and z2 = 4 – 7i. Express in the form of x + yi where x and…

A: We have to solve given problems:

Q: Let z be a complex number. Then the solution(s) of sinhz+coshz=1/e is (are) * Z=-1 does not exist…

A: Given, z be a complex number. we need to find the solution of sinhz+coshz=1e

Q: Let z be a complex number. Then tanh(2+ Ti) is equal to * cothz O -tanhz -cothz None of these O…

A: according to bartleby guideline, I can solve first question...

Q: Let z be a complex number. Then the solution(s) of sinhz+coshz=e is (are) * O z=1 None of these does…

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Q: Let z be a complex number. Then coth(2+ Ti) is equal to None of these -tanhz tanhz cothz -cothz

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Q: 1. nRoots of complex numbers 1. Find the 3roots of z1 = 1+ iv3.

A: YOU HAVENT MENTIONED THE PART THEREFORE DOING JUST FIRST.     1)  First we will calculate the nth…

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: Determine real and imaginary component of function sinh(x). Prove that sinh(x) is holomorphic in…

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