Let z be a complex number. Then sin (3z) -i is bounded in C . TRUE OR 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: et P(x)=2x^4+9x^3+13x^2+81x-45 Factor p(x) over the complex numbers

A: We have fx=2x4+9x3+13x2+81x−45Put…

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

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Q: Let z be a complex number, and w be its additive inverse. Let c be another complex number. If |zc| =…

A: Given z be a complex number and let w be its additive inverse. ⇒z+w=0 and z=w, argz=argw+π Given…

Q: Express the complex number z =1- 3i in the form of ree and deduce the following complex numbers in…

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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: Find the midpoint of the line segment joining the points corresponding to the complex numbers in the…

A: The point corresponding to -1 - (1/4)i is= (-1, -1/4)  The point corresponding to 3/2 + (3/4)i is=…

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

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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…

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Q: Plot the number 1 + 2i on the complex plane.

A: 1+2i has the real part 1 and imaginary part 2. As the x-axis represents the real part and the y-axis…

Q: The complex number Z1and Z2 are given by, Z1 = 3 – 5i and Z2 = -1+ 4i Determine: 2Z1 +5Z2

A: We have to determine 2Z1+5Z2 for the given complex numbers: Z1=3-5i and Z2=-1+4i Finding 2Z1:…

Q: What is the result of multiplication of complex numbers -V3+i and (cos + i sin )? 3

A: Let z_1 = - sqrt 3 + i = r cos theta + i . r sin theta r cos theta = - sqrt 3 r sin theta = 1 Then…

Q: Find the quotient z1/z2 of the complex numbers z1 = 2 + 2i and z2 = 1 + i. Leave answers in polar…

A: Given: z1=2+2i , z2=1+i To determine: z1z2. Also, to write answer in polar form.

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: 2Q Express the complex number 1+ 3i in the form x + yi, where x and y are real numbers. 1-2i

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Q: Rewrite the complex number 5(cos5.5+i sin5.5) in a+bi form

A: See the details solution below

Q: Determine the absolute value of the complex number z = 3 + 4i

A: Given: z=3+4i

Q: snip

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

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: 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: 3. Determine all complex numbers z for which |2z – 1| < 2|2 – i|.

A: The given problem is to find all the complex numbers that satisfies the given complex inequality.

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

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Q: Find all complex numbers satisfying |z + 3 + 4i| = |z − 5|

A: Topic:- complex numbers

Q: a) Let a complex number z =-5i+3. Find in the standard form x+ yi . IN

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Q: snip

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Q: Present complex number z in algebraic form =* + 23D 35 1-3i

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Q: The complex number Z1 and Z2 are given by, Z1 = 3 - 5i and Z2 = -1+4i %3D Determine: 2Z1 +5Z2

A: topic - complex numbers

Q: The real part of the complex number z = (2+2i)² + e¹+2i is

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Q: Find the quotient z1/z2 of the complex numbers z1 = 50(cos 80° + i sin 80°) and z2 = 4(cos 25° + i…

A: We have to find quotient z1z2 of the complex numbers: z1=50cos 80°+i sin 80° and z2=4cos 25°+i sin…

Q: If |x = 3i| <5, then prove that the complex number z also satisfies the inequality i(z+1)+1| <25.

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Q: 3. Having two complex numbers z1 & z2, with product z,z2 being real and non-zero, verify if there…

A: Answer is following .

Q: Find the product of the complex number z = 3 + 4i and its conjugate z*.

A: The complex number is given as z=3+4i

Q: Let z be a complex number such that z, z3 and z5 form an equilateral triangle on the complex plane.…

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Q: Use DeMoivre’s theorem to find z4, if z is 1 + 1i. Express your answer in complex form

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Q: Let the left complex number be z1 and the right complex number be z2. +i sin- 43 - 4i 8 cos a) Write…

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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 midpoint of the line segment joining the points corresponding to the complex numbers in the…

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Q: Z is a complex number

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Q: Let z = 3 – Ai, w = 1+ 2i be complex numbers. For both z and w, what is the: • Real part • Imaginary…

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Q: The reciprocal of a complex number x+jy is

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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: Find the complex conjugate of (2+3i)/(1-i)

A: We find complex conjugate of (2+3i)/(1-i)

Q: The complex number z=2eiπ/4 can also be written as z=√2i z=√2+√2i z=2+2i z=√2

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Q: Determine the absolute value of the complex number z = 5 + 12i

A: We have to find absolute value of complex number: z=5+12i We know that if we have complex number…

Q: 2. What is the standard form of the complex number –13.5(cos() + i sin())?

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Q: It is given that z = x+ iy where x and y are real numbers. Find the complex number z such that z+3z…

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