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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...

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.

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 ...

y''=d 2 y/dx 2 , y'=dy/dx for ease of writing First off split the full equation into th homogeneous equation and the particular function. The homogenous equatiion is when our collection of y, y', y'' are on ...

We have that the Taylor series of a function infinitely differentiable at a x = a is given by the expansion: f( x ) = f( a ) + f'( a )( x - a ) + f''( a )( x - a ) 2 /2! + f'''( a )( x - a ) 3 /3! + f (4) ( ...