6.96. Expand each of the following functions in a Laurent series about z -0, naming the type of singularity in each case (d) ze-t (b) ez/Z3, (a) (1- Z-l cosh z-1, 4 (c) cos Z)/Z,

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: 3 2 f(x) = 2x -x + 11x² - 4x+12

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Q: What we want to do next is to write a procedure to raise any complex number to any integer power (x…

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Q: Use Descartes's rule of signs to obtain information regarding the roots of the equation. (Select all…

A: By using Descates's rule of signs to obtain information regarding the  roots of the equation.…

Q: Determine the roots of y"" - 4y" + 3y = 0

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Q: Let zand w be complex numbers with the following properties. |z| = 7, |w|= 3, Arg(z) = − and Arg(w)…

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Q: . Define complex variable and complex conjugate with example

A: Topic = Complex number

Q: How would I find the magnitude of the complex number based on the given values for z?

A: To find the magnitude of the complex number

Q: 4. Find all solutions in the complex numbers to the following equations. (a) z5 = z. (b) 24 = iz².

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Q: (x + 5)(x - 2)dz Find + C

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Q: Number 8

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Q: Divide. -2i 2+3i Write your answer as a complex number in standard form.

A: The given complex number division -2i2+3i. We have write the number in standard form.

Q: 1. Let z and w be complex numbers. (a) Show that |1+ z w² + |z – w2 = (1+|z|?)(1+ |w/?). (b) Show…

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Q: Solve the complex number z = (2+3i)^3/2

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Q: Find the indicated roots and graph them in a complex plane URGENT PLEASE

A: First we have to convert given complex number into 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 4,,2 are two complex numbers then : ollz|-|z||>|z1-z |z,+z2ls\z]\+|z3l |

A: If z1,z2 are two complex numbers, then (a) z1+z2=z1+z2 (b) z1-z2>z1-z2 (c) z1+z2≤z1+z2 (d)…

Q: Are operations with complex numbers similar to operations with polynomials?

A: When a negative number is expressed inside the square root operation, the imaginary unit i=-1 is…

Q: Question 5: The roots of the equation 1 4 20 1 -2 = 0 = 0 are 5x² %D 1 2x

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Q: Find all complex numbers w such that w ² = -1

A: Given that The nth root of the complex number  is

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: Z is a complex number

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Q: Express the result in trigonometry and rectangular form (1 + 2i)4 44. (1 – 2i)?

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Q: Ex : find the real part of analytic complex variable if imaginary part of it is v = (xy) V%3D

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Q: Find the cube root of Z^3=8i lying in the first quadrant of the complex plane. " i-V3 O 2i+v3 i+2/3…

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Q: a

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Q: Show that the solution of the equation  4x2 + 24x + 37 = 0 are complex conjugates of each other.

A: Given quadratic equation: 4x2+24x+37=0