4. Show that any complex number of norm 1 (except -1) can be written in the form z = (1 + it)/(1 − it) for some t E R.

Q: If z1,72,., are complex numbers such that = =.==,| =1,Prove that 1. 1 1

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Q: a) Show that if you have a complex number z, then Re(z) = (z+z*)/2. Now show that Im(z) =…

A: Since you have posted multiple questions with multiple sub parts, we will provide the solution only…

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: Write down monic polynomials in R[X] of least possible degree which have the following complex…

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Q: Let x₁, x₂ are the roots of the quadratic equation x² + ax + b = 0, where a, b are complex numbers…

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Q: Let z be a non-zero complex number. Then Log(z²) = 2Logz ) None of these O if OSArg(z)ST/2 O if…

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Q: Let z1 and z2 be complex numbers. Which of the following statements are always true? (i) Re(z1z2)…

A: Complex analysis, modulus of the complex number

Q: Prove that the roots of X2+(1-K)x+k-3=0 are real for all values of k?

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Q: (a) (b) (c) (d) (1+2i) ² 2 1/(1+i) √3-4i ein/4

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

A: Let z be complex number then

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

A: Given a statement

Q: Let z be a complex number. Then the solution(s) of sinhz+coshz-e is (are)* None of these z=nti+1…

A: See solution below

Q: #2. If 2₁ and 2₂ are two complex numbers, show that 12₁-221² + 12₁ +221² = 2 ( 1211² + 122 1²).

A: 2. Let z1 = a + bi and z2 = c + di be two complex numbers.      Then,          |z1|2 = a2 + b2…

Q: Determine, with justification, all complex numbers z that satisfy z²(z)4 Simplify your answer(s) as…

A: The given expression is: z2z4=i