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By definition z*  = a - bj.

We can write z/z* = ((a+bj)/(a-bj))*(a+bj)/(a+bj).

We calculate this to be z/z* = (a^2-b^2)/(a^2+b^2) + j(2ab)/(a^2+b^2).

Therefore, Re(z/z*) = (a^2-b^2)/(...

Multiply by complex conjugate

z = 50 / (3+4i) * (3-4i) / (3-4i)

Rationalise

z = 50 ( 3 - 4i) / 25 = 6 - 8i.

Let's say that T is a transformation of the two dimensional plane. Remember that we have the two standard unit vectors (1,0) and (0,1). These are, respectively, the unit vectors pointing in the positive d...

d²y/dx² - 8 dy/dx +16 y = 2x Auxiliary Equation: m² - 8m +16 = 0 (m - 4)² =...

i. P(AuB) = P(A) + P(B) - P(AnB) 

P(AnB) = P(A|B)P(B) = 0.3P(B)

P(AuB) = P(A) + 0.7 P(B) --> 0.6 = 0.2 + 0.7 P(B) --> P(B) = 4/7

ii. P(B'|A') = P(A'nB')/P(A')

P(A'nB') = ...