(a) The Argand diagram shows complex numbers w and z with arguments and respectively, where <0. The area of the triangle formed by 0, w and z is A. 0 Show that zw - wZ = 4iA. 0 Ø Muscal W

Q: find all complex Values satisfy ing the given equation ē = 2+1 (-1+i) .

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Q: 3 lim Z→2 (Z-2)4 ∞

A: We have to find the limit.

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: Numerical results should be rounded to two decimal places. Identify the set of complex numbers that…

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Q: Z is a complex variable z=x+iy  question attached as photo

A: The function is given as

Q: Q3: (a) In the metric space (S, d), Vx,y ES. If A = where S = [0, 1]; d(x, y) = |x-yl; A = [0,2),…

A: A metric space is a set together with a metric on the set. The metric is a function that defines a…

Q: Z is a complex variable z=x+iy  question attached as photo

A: The closed integral is

Q: z is a complex variable z=x+iy question attached in photo

A: As per norms, the first three parts A, B and C are solved.To test if the given function is harmonic…

Q: find quotient 1/z for given complex number z=-sqrt 3 + i

A: The given complex number is z=-3+i. The conjugate of the given complex number is as follows. z=-3-i

Q: Z is a complex variable z=x+iy  question attached as photo

A: We know some general Laurant series expansion of ex,cosx,coshx as following :

Q: Let z be a complex number. Then coth(2+7ti) is equal to cothz -cothz tanhz None of these -tanhz

A: Solution

Q: (d) Let Z₁ = −4+ 8i and Z₂ = -1 -2i. Show that (i) 21/2₂ | = 4. | (ii) (iii) |z₁|² +Z₁ Z₂ = 100.…

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Q: Z is a complex variable z=x+iy  question attached as photo

A: Consider the closed integral

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

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

Q: Z is a complex variable z=x+iy  question attached as photo

A: The area enclosed by a simple closed curve,

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: What is the image of the line x = c; c > 0 in the function f(z) = ? ("z" complex number) Z

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Q: Write the following complex numbers in rectangular form (z = x + iy) el-i +1 el-i – 1'

A: I have divide each terms as a+ib form the rationalized

Q: Z is a complex variable z=x+iy  question attached as photo

A: As per norms, the three parts a, b and c are answered.  To identify the sets (regions) defined by…

Q: 16.(Honors Class Only)Rewrite each of the following expressions involving complex numbers in the…

A: This question is based on Complex Number multiplication.

Q: Select the correct answer. Convert 1 + i to polar form. ⒸA. √2cis ³ 3x OB. √2cis c. √2cis D. √2cis0

A: 1+i

Q: Complex Numbers. Find, in the form x + iy, showing details, 11. (2 + 3i)2 12. (1 – i)10 14. Vi 13.…

A: Dear student, as per our company guidelines we are supposed to answer only first 3 sub-parts. Kindly…

Q: Identify the set of complex numbers that satisfies the condition.  z* = z1

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Q: Let z be a complex number. Then cot(5z-pi)=coth(5z)?

A: According to the given information, it is required to check whether the given statement is true or…