z = r(cos 0+isin 0).

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

A:

Q: B- If x+= = 2 cos Ø prove that x"+ 2 cos rø by used complex number.

A:

Q: If z,,z, are two complex numbers then: ||z.|-|z2||>|z,-z z. +z_ s z +z]. z +z_ = z +/z

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Q: Find the quotient z1/z2 of the complex numbers z1 = 12(cos 3π/4 + i sin3π/4) and z2 = 4(cos π/4 + i…

A:

Q: Find all the complex cube roots of w=8(cos210°+isin210°). Write the roots in polar form with θ in…

A: This question is related to complex numbers, we will solve it using given information.

Q: Let z be a complex number with |z|=17 and let z0=17−11i . What is |z−z0|^2+|z+z0|^2 ?

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Q: The set of all complex numbers is denoted by C={x+iy:x,yER} ylgn O ihi O السؤال 2 lim does not exist…

A: Every complex number is x + y i , where x and y are real number So statement is True.

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

A:

Q: If the complex number z = x + iy satisfies the condition |3z – 6i| = 3 , then z lies on Oa. a.…

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Q: 4. If the two complex numbers z1=ri(cos01+ i sin 01) and z2= r2(cos 02+ i sin 02) then the numbers…

A: The given complex numbers,z1=r1cosθ1+i sinθ1 and z2=r2cosθ2+i sinθ2

Q: B- If x+ 2 cos0 prove that x" +2 cosro by used complex number.

A: we have to show that the following

Q: let 2=x+iy be a complex number soch that coshe hen Im(tanhe) is equal to sinhycoshy sinh?x+cos²y

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Q: Let z be a complex number. Then Im(-iz+1)= * O =liz-1| O None of these Ozliz-1| Sliz-1|

A: The last option is correct.

Q: When a complex number z is written in the polar formz = r(cos θ + i sin θ), the nonnegative number r…

A: Given- When a complex number z is written in the polar form z=rcosθ+isinθ, the nonnegative number r…

Q: If the complex number z = x + iy satisfies the condition |3z - 6i| = 3, then z lies on a. Circle…

A: We know that z=x+iy and z = x2+y2 Then 3z-6i = 33(x+iy)-6i = 33x+3iy-6i = 33x+(3y-6)i =…

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: Write down the definition of the complex conjugate, ž, of z = a + ib where a, b are real number…

A: Complex conjugate of a complex number z is defined as a complex number which has same real part as z…

Q: Find the modulus and argument of the following complex number. z=(3-2j) (1+2j), giving the principal…

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Q: Express the complex number z = 4 – 4/3i in polar form r(cos 0 + i sin 0). Select the correct answer…

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Q: Let z be a complex number .then cos (3z)-I bounded or not

A: Substitute z=x+iy, then convert into real and get known real valued function which is unbounded.

Q: Write the complex number z = 2 - j2 in polar O 2.83245° O 2.832-315° O 2.832-45° O -2.832-45°

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Q: Write down the definition of the complex conjugate, z, of z = a + ib where a, b are real numbers.…

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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: Let z be a complex number. Then the solution(s) of sinhz+coshz=1/e is (are) * None of these does not…

A:

Q: 2. Find the Cartesian (x+iy) form of this complex number 3π 3π Z=4(cos + 2 isin 377)

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Q: B- If x+! += 2 cos prove that x"+= 2 cos rø by used complex number.

A: we have to show that the following

Q: Let z be a complex number. Then cot(5z – n) is equal to

A: Since solve the first question for you. If you want any specific question to be solved then please…

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: Find the quotient z1/z2 of the complex numbers z1 = 20(cos 75° + i sin 75°)z2 = 4(cos 25° + i sin…

A: Given complex numbers,  z1 = 20(cos 75° + i sin 75°) z2 = 4(cos 25° + i sin 25°) To find z1/z2

Q: Find the points of intersection between r =2 cos20 andr=- %3D 1- cose

A: To find the intersection point two curve we have to find r,θ by solving given curve.

Q: Let z be a complex number. Then Im(-iz+1)= * O =liz-1| None of these O 2liz-1| <liz-1|

A:

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

A:

Q: Let z be a complex number. Then i(cosh(3z)+sinh(3z))=e^(3z)?

A: Explanation of the answer is as follows

Q: Let z be a complex number .then e^(3z+i) is bounded over the set of complex numbers?

A: Let z is a complex number. Let f(z) = e(3z+i)  Let us assume that f(z) is bounded. Hence f(z) is an…

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

A: Given that z is a complex number. we have to find such z so that                              sinh…

Q: Find all complex numbers z of the form 2 =x+iy such that that ZZ = = 25 and *+ y = 7.

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Q: Express the complex number z = -V2 - V2i in polar form r(cos 0+i sin 0). Select the correct answer…

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

A:

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 the solution(s) of sinhz+coshz=e is (are) * O z=1 None of these does…

A:

Q: Let z be a complex number such that Iz| = 4 and arg(z) = 5Tt/6, %3D * = then z

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Q: Find the quotient z1/z2 of the complex numbers z1 = 5(cos 4π/3 + i sin 4π/3)z2 = 10 (cos π/3 + i sin…

A: Given,   z1=5(cos4π3+i sin4π3)  andz2=10(cosπ3+i sinπ3) To find quotient z1z2: We know that,…

Q: Let z be a complex number. Then cos(tz)+3i is unbounded in C. * False True

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

A:

Q: what are the complex numbers z1 and z2? for z1 i got z1= 3(cospi/12 + isinpi/2), z2= 2(cos7pi/12 +…

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Q: Let z2 = -V2 + i/3, w = -3+ 3i and p= -3– 2i. 1. Find all the complex numbers given by In z2.

A: It is given that