Recent content by loy

welcome dude !

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 +...

thanks dude , i found the answer!

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.

you mean multiply the conjugate of 2+cos(θ)+isin(θ) in order to find the x and y?

how to do equating the parts? they are cos and sin there.

not given , my lecturer just gave me the question as I've written above. So, what should I assume?

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...

thanks very much =)

help me ~~~

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...

yup,you've got it~ erm...sigh...i am sorry ,the main problem is i don't know the answer... so , i need your help~

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...