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

A:

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: #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…