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

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

A: See solution below

Q: Let z is a complex number and Z is the conjugate number of z then () equals O a. z1 Z2 b. 21 Z2 C. O…

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Q: The complex number u = a + bi is an ________ ________ of the complex number z when z = un = (a +…

A: Consider "The complex number u = a + bi is an ________ ________ of the complex number z when z = un=…

Q: Let a, b, and c be any three nonzero complex numbers. If |z| = 1 and 'z' satisfies the equation az +…

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Q: Rewrite the complex number 3(cos 3.5 + i sin 3.5) in a + bi form a = b =

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Q: Let z be a complex number satisfying 12|z|2 = 2|z+ 2|² + |z² + 1|2 + 31. What is the value of z + °…

A: Given, 12z2=2z+22+z2+12+31 Now solving the given equation as,…

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

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Q: Given that the complex numbers zı and z2 are such that z, = cos 10° + i sin 10° and z2 cos 15° + i…

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Q: 3. How may the following complex numbers be obtained from z = x + iy geometrically? Sketch. а. 2 b.…

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Q: Let z be a non-zero complex number. Then Log(z?)= 2Logz for all complex numbers O rosArg(z)st…

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Q: The modulus of the complex number z = 1- e" is A 2sin (0) B. 2 cos (e) В. C. 2 D. 1

A: We have to find the modulus of the complex number z=1-eiθ.

Q: 30. The complex number 1 + V3i can be expressed in exponential form as 2e A в 2e- is 2e- 2e D

A: In the given question we have to expressed the complex number z in the exponential form…

Q: 3. How may the following complex numbers be obtained from z = x + iy geometrically? Sketch. а. 2 b.…

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Q: The ________ ________ of the complex number z = a + bi is z = r(cos θ + i sin θ), where r is…

A: z=a+ib be any complex number

Q: Let z be a complex number. Then cos(32)-i is unbounded in C. * False True

A: use:- cos(x+iy)=cosxcoshy−isinxsinhy

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

A: From Liovilles thm we can say Every non constant entire function is unbounded.

Q: 6. Find the following complex numbers in the form r+ iy, whe and y are real. (i) (3+7i) + (6 – 10i)…

A: we have to find complex numbers in the form of x + i y  Adding real part with real part and…

Q: If 5 and 2 are complex numbers, then prove: (a) l-k|| (b) (c) +s|s|+|=|

A: I have solution for (a), and (b) a ..

Q: If z is a complex number then the sum of z and its conjugate is an imaginary number. O true false

A: Let z be a complex number given by, z=a+ib where a is the real part and b is the complex part of z.

Q: Let A, B, C be the set of complex numbers defined as: A = {z: | z+2|-|z- 2 || = 2} 6. %3D z-1 TC B =…

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Q: The set of all complex numbers is denoted by C={x+iy:x,y€R}

A: A complex number is the combination of real and imaginary number in the form of x+iy , x, y are real…

Q: The roots of the complex number z = (2)¹/2 is Wo = √2 [cos+ i sin], w₁ = √2 [cos+ i sin true false

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

A: Let z be complex number then

Q: snip

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Q: 18 Given the complex number z = i, £$=:(2)" = A 1+i -i C -1 +i D -1

A: Topic : complex number

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

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Given the complex number z such that z-4i = a+3zi , find the value of a if z is purely imaginary.

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Q: z=x+i y geometricaly ?

A: Given: a) z¯ b) -z c) 1z To find: The complex number obtained from geometrically.

Q: .2 Describe and give the geometric representation of the following point set of complex numbers S=…

A: We shall solve this in next step in details

Q: Express the given complex number in rectangular form (a + ib). T 1. + i sin + i sin cos 9. 9.

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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: 17. The argument of the complex number z. where com CO is 1- i 13

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Q: Let z be a complex number. Then cos(72)+3i is unbounded in C. False True

A: this is true , because

Q: 1 If a complex number z satisfies | -3 | z+3 find the largest %3D sin75 ° cos75°* Value of | z+i|.…

A: We are given that a complex number z satisfies z-3+z+3=1sin75∘ cos75∘ . So,…

Q: Let z be a complex number. Then cos(72)+3i is unbounded in C. * O False True

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Q: Given the complex numbers z1 = -3+i and z2 = 1+ 4i. Show that |z1 z2 = |z1||22| and org (z1 2) = arg…

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Q: 1. Given the following complex numbers: Z1 = 2 – j, z2 = -3+ j4, z3 = -5 – j6, z4 = 2 + j3 %D…

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Q: A. Express the following complex numbers in standard form. 1. z = 0 + 2.1=-2+4 2

A: Introduction: There are many different representations of a complex number. But, the standard…

Q: Q4\ If z and z are conjugate complex numbers, find two complex numbers, z = z, and z = z,, that…

A: The given equation is: 3zz¯+2z-z¯=39+i12 Let z=a+ib be a complex number satisfying the equation,…

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

A: Assume sin3z is bounded. We know that sin3z is analytic on C, that is sin3z is an entire function.…

Q: Derive the formula for the cos'(z), where z is a complex number.

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Q: (b) Calculate (i) z1 + Z2. (ii) z, Z2. (iii) z1/z2.

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

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

A: Given problem is :

Q: It is given that W = 2+ 2i, z + 2i = iz + X, Imw = 8, where z and w are complex numbers, and is a…

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Q: Let z be a complex number. Then e32+ is bounded over the set of complex numbers. a. True b. False

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Q: Which of the following is equal to the complex number z = O v5(1+ j) O -5 O 5j O none of the above

A: Here we solve the problem by using the absolute value and angle form of the complex numbers as :

Q: For any complex number Z, Je²| > 2 if Re(Z) > 0 Im(Z) > 1 • |z| 1

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