the solution is like this
3/[2+cos θ+i(sin θ)]
= [3(2+Cosθ)- 3 Sinθ i] / [(2+cos θ)^2 + (sin θ)^2]
So, from LHS, we get
x=3(2+Cosθ)/ [(2+cos θ)^2 + (sin θ)^2] while
y=3 Sinθ/ [(2+cos θ)^2 + (sin θ)^2]
On LHS: x^2+y^2
=[9(2+Cosθ)^2+9Sinθ^2]/ [(2+cos θ)^2 + (sin θ)^2]^2
=9/[(2+cos θ)^2 +...
but as long as x>0 , y can be defined in any value in R.
given x>0,
IF y>0 , f(x,y)=x^y .
IF y<0 , f(x,y)=x^(-y) = 1/(x^y)
IF y=0 , f(x,y)=1.
BUT when x<0 , the function is not defined , meaning , you can't get any answer, the function is discontinuous in x<0.
the domain of x is (0,∞)...
see this If z=x^y, then ln(z)=yln(x) , x cannot be less than zero since x is not defined if it is less than 0 . if you don't believe, you can press your calculator to see whether it has a result when you put in x a value which is less than 0.
Homework Statement
Given that, x+yi=3/[2+cos θ+i(sin θ)] , prove that x^2+y^2=4x-3
Homework Equations
r^2=x^2+y^2
The Attempt at a Solution
since we know that x=r sinθ , y=r cosθ,
i multiply r on the right hand side to equal 3r/[2r+x+yi], then multiply its comjugate (2r+x)-yi to...
Homework Statement
i recently saw a question about complex number, and its answer about the center of a circle is 1/2*(1+i). what does that mean?
Homework Equations
f:ℂ → ℝ^2
The Attempt at a Solution
since we define z=x+yi is an element of ℂ, so by the mapping above,
we can say...
okay,i have learned some basic theorem(like bernoulli's equation,stokes' law) about the pressure,but i don't know which 1 should be used since i have never met the question which needs to calculate the pressure of fluid with 1 input and 3 outputs.all i know is the dV/dt of input and output are...
hi,tim~
the water is moving,but i only know the pressure of water pump is 8 bars and the diameter of the pipe which is connected to the pump is 2 and 1/2 inches.
there are 3 pipes connected to the previous pipe,3 of them are 1m long,1 is above the ground(d=1/2 inches) and another 1 is...