Let z1 and z2 be complex numbers. Which of the following statements are always true? (i) Re(z1z2) (ii) |Im(z1) + iRe(z1)l = Iz1| Re(z122) %3D (iii) If z1 = rje", z2 = IT ', z1 = z2, and 0 is the principal argument of. Z1 then 0 %3D 8

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A: Given equation : 2r+3s=29 3r+2s=16   Use Cramer’s Rule to find the values of r, s rDr=-sDs=1D

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A: 4) a) Given:          cube roots of -8i we write in trigonometric form:          =8cos-π2+isin-π2 we…

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A: Evaluating the value of the expression

Q: using Cramer's method

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A: Since you have uploaded multipart question, according to our guidelines we have solved first three…

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Q: Q1) Find the inverse of A (1 00 A=2 1 0 5 4 1

A: A=100210541

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A: (BA)T - ATBT + AC = AC In LHS, We know that, By the properties of Transpose, (BA)T = ATBT .…

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A: Here we have to find which of the options are multiplicative inverses.

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A: Given: |z+3|+|z-3|=10

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A: The given function is,

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A: We can solve this as follows:

Q: 2. (a) Show that (z − 1)(26 + 25 + 24 + z³ + z²+z+1) = z7 - 1. (b) Show that if ¢ is a 7th root if…

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A: Given  z=1−2jw=2−3j

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Q: (9x – 10x – 4x2 + 2x) – (4x° – 9x* + 2x² – 6) O 5x* + 9x* – 10x³ – óx? + 2x + 6 O 5x° – 9x* – 10x³ -…

A: The given expression is: (9x5-10x3-4x2+2x)-(4x5-9x4+2x2-6)

Q: A=[1 -3 -5 -8]      [0 5 -5 -6]      [0 0 -4 -5]      [0 0 0 4] Inverse of the following matrice

A: use the concept of  A = IA