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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 ...

Answered by Chris S. • Further Mathematics tutor

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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

Answered by Jakob S. • Further Mathematics tutor

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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 an...

Answered by Jakub W. • Further Mathematics tutor

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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.

Answered by Tutor80806 D. • Further Mathematics tutor

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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 t...

Answered by Martin S. • Further Mathematics tutor

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