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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 =...

Firstly you should expand the brackets in this situation in order to collect the like terms, so get all the x's on one side and all the constants on the other side of the inequality. Expanding the bracket...