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Given that z = a + bj, find Re(z/z*) and Im(z/z*).

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)/(a^2+b^2). Im(z/z*) = (2ab...
PJ
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z = 50 / (3+4i). What is z in a+bi form?

Multiply by complex conjugate z = 50 / (3+4i) * (3-4i) / (3-4i) Rationalise z = 50 ( 3 - 4i) / 25 = 6 - 8i.
IM
7968 Views

How do you find the matrix corresponding to a transformation?

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 dire...
RF
3145 Views

Find the general solution to the differential equation: d^2y/dx^2 - 8 dy/dx +16y = 2x

d 2 y/dx 2 - 8 dy/dx +16 y = 2x Auxiliary Equation: m 2 - 8m +16 = 0 (m - 4) 2 = 0 m = 4 (repeated root) Complimentary function : y = (A+Bx)e 4x Particular integral : try y p = ax + b dy p /dx = a d 2 y p /d...
OF
9395 Views

How to solve the inequality 1 - 2(x - 3) > 4x

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 yo...
FE
4481 Views