Top answers

Given z=cosx+isinx, show cosx=1/2(z+1/z)

We first consider 1/z=(cosx+isinx)^(-1). Application of De Moivre's theorem for integer n: (cosx+isinx)^(n)=cosnx+isinnx yields the result 1/z=cosx-isinx. Addition of the two forms z and z^(-1) steers us to ...
CS
9677 Views

Find the square root of complex number 3 + 4i

Strategy: write down an equation satisfied by the square root, and solve it algebraically. Method: square root x+iy satisfies (x+iy) 2 = 3 + 4i. Expand: x 2 -y 2 +2xyi = 3+4i. Comparing coefficients gives: x...
JS
29140 Views

Which test for convergence is the best for which series?

In IB Calculus Option you are introduced to number of different tests. They are Divergence Test, Comparison Test (simple and limit forms), Absolute Convergence Test, Alternating Series Test, Ratio Test and I...
JW
3247 Views

Show that cosh^2(x)-sinh^2(x)=1

In exponential form, sinh^2(x)=1/4(e^2x+e^-2x-2), cosh^2(x)=1/4(e^2x+e^-2x+2). Therefore cosh^2(x)-sinh^2(x)=1/4(2-(-2))=4/4=1, as required.
TD
11021 Views

Why is the argument of a+bi equal to arctan(b/a)?

Think about the point a+bi on the complex plane. Specifically, a is how far along the x (real) axis, and b is how far up the y (imaginary) axis the point is. If you draw a line connecting the origin and the ...
MS
15972 Views