complex numbers.

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: Find the 5™ roots of the complex number [(2+x) – 5i] , where x = last digit of your ID Number.

A: To find- Find the 5th roots of the complex number 2 + x - 5i, where x = 2

Q: Represent the complex number geometrically.(1 + 2i)2

A: Represent the complex number geometrically.(1 + 2i)2

Q: Suppose Zi and Z, are two given complex numbers. Construct graphically a. 3Z1 – 2Z2 b. (1/2)Z, +…

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Q: Write the complex number in polar form with argument 0 between 0 and 2n. -1 - V3i

A: Given query is to write the expression in Polar form.

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

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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: Let , ² be the complex cube roots of unity. Let z₁, Z₂, Z3 be complex numbers such that Z₁ + Z₂ +Z₁…

A: Given that, Let ω,ω2 be the complex cube roots of unity. Let z1,z2,z3 be complex numbers such that…

Q: Use DeMoivre's Theorem to raise the complex number to the given power. Express your solution in…

A: Compare the given complex number with the standard form and find x and y.Find theta using x and y.

Q: 5. Determine the roots of the complex numbers studied in class. z³ = 2 – 3i

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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: Divide the following complex numbers: (ComplexNumber)1 (ComplexNumber)2 1. (ComplexNumber)1: Real X1…

A: given that

Q: of the complex number: (27V3 27 3

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Q: iv) in complex number z3. (7)? = |z|?. z

A: Complex number: A complex number has the form z=x+ιy, where x is called the real part and y is the…

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: Find all the roots of the complex numbers using different theorems. 1 1. (-5 +j12)5

A: Let's find.

Q: Find the roots of the given complex number 1. z^3 = -2

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Q: Suppose the product z1z2 of two complex numbers is a nonzero real constant. Sho 2 kz1, where k is a…

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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: Take the last four digits ABCD of your student identification number, and let z1= A + Bi and z2 = C…

A: Here, z1=5i z2=6+4i

Q: Use DeMoivre’s theorem to find (–√3/2 +i/2)12. Express your answer in complex form.

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Q: Show that if z1 and z2 are complex numbers, then zi + z2 = Zī + Z2.

A: Suppose the two complex numbers are z1 and z2 such that where a,c are real parts and b,d are…

Q: Express the complex number in trigonometric form with 0 ≤ θ < 2π.-17

A: Let z=−17⇒z=−17+i0The complex form z=x+iy in trigonometric form is written asz=rcosθ+isinθ,…

Q: What is the complex conjugate of 2 – 3i ?

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Q: If z is a complex number, show that the sum of z and its conjugate is a real number.

A: Given z is a complex number. Let z=x+iy We know that conjugate of a complex number is given by…

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: 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: 5. Determine the roots of the complex numbers studied in class. z3 = 2 – 3i %3|

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Q: If 21 and z2 complex numbers such that z1 = 1+ V3i and 22 = V3+ i determine in polar form, (i) ž122…

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Q: Write the complex number z=(1-√3i)2015/(√2cis(7π/6))4028 in an exponential form.

A: cis(x) = cos(x)+isin(x)

Q: Find the real and imaginary parts of the complex number.

A: Given complex number: i3

Q: - Find the roots of the following complex nos. 3. %3D 3. Z =\ Z-27-0 %3D 3. |

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Q: 1. Write the complex number 2+ iv3 in the form of reio . (2 Marks)

A: Here we first find modulus and arg then convert this into polar form

Q: Convert to complex form z3 = 8

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Q: If the complex number Z=2+2√3i .then r=

A: We know that , If z=a+bi then r=a2+b2

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: Write the complex number in polar form with argument 0 between 0 and 2m. -VZ+ V6i

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Q: If a, b, c, d are complex roots of x 4 + 2x 3 + 3x 2 + 4x + α = 0 and ab = cd, the value of α is…

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Q: Suppose Z, and Z, are two given complex numbers. Construct graphically a. 3Z1- 2Z2 b. (1/2)Z,…

A: Suppose complex number Z1=a1+ib1=2+3i and Z2=a2+ib2=-1-2i (a) given complex number 3Z1-2Z2…

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

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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: 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 as complex number a. (V(9) - v(-9))*( v(-36) b. V(-16) *(V(25) - V(-25) ) c. (3+ 2v(-9) ) *…

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Q: complex numbers. Construct graphically

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Q: If the complex number z = x + iy is a solution of the equation z2 + z + 1 = 0 then show that z = x…

A: z2 + z + 1 = 0 Solve the given equation using quadratic formula…

Q: Prove that x^2 = 4 will result into ± 2 using complex numbers.

A: Given that, x2=4

Q: Exer. 21–46: Express the complex number in trigonometric form with 0 so<27. 25 2V3 + 2i 4 cis 37 29…

A: Given: The complex number 25) 23+2i. 29) -20i 34) -5.