2πT Let S = {n= (1 + i)(w7)" | n € N} where w7 = exp(i- Show that S is the collection of all 7th roots of a complex number zo = a+bi. What is the complex number zo ? Determine the accumulation points of the set S. Justify your answers.

Q: Let w = Reai be any nonzero complex number. Then w has n nth roots: n solutions to the equation z" =…

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Q: If z1 and z2 are complex numbers such that |21| = |2|, prove that arg(2122) = arg ((21 + z2)²) .

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Q: 11. Write the quotient of the complex numbers in the standard form z=x+ iy. 3+i 1-2i

A: If you like the solution then please give it a thumbs up.... The Answer is:           Standard form…

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

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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

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A: according to our guidelines we can answer only three subparts, or question and rest can be reposted.…

Q: 1. Describe and sketch each of the following sets of complex numbers: (a) 1 0 (d) |z −1²+ |2 + i|² <…

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Q: Let z be a complex number. Then sinh(2z)-i is bounded in C.* False True

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Q: bers are conjugate. If z, and z2 are two non-zero complex numbers st jal arg (2) ) - arg (z2 ).

A: Since we know that, | Z1 + Z2 | = |Z1| + |Z2| only when the the point Z1 , Z2 and origin are…

Q: Let x₁, x₂ are the roots of the quadratic equation x² + a where a, b are complex numbers and y₁, y2…

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Q: If a and b are complex numbers, prove that |a+b|<\a|+\b| .

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Q: If z̟ = 1 + jb , z2 = re¬j² , z1/z2 = -10, determine all possible values of b and r.

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Q: C. Find all complex numbers z of the form 2=x+y such that that zz = 25 and *+y = 7.

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