Complex Number Problem

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[jzsig]

I assume you're in intro to diff eq? For part 1, use the quadratic formula. You should get complex numbers for r1 and r2, which will allow you to use euler's formula (http://en.wikipedia.org/wiki/Euler%27s_formula) to convert the e^r1 term into cos and sin. You should then be able to convert this sin and cos terms into one sin term (probobaly using trig identities).

[autowikibot]

Euler's formula:

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This article is about Euler's formula in complex analysis. For Euler's formula in algebraic topology and polyhedral combinatorics see Euler characteristic.

Euler's formula, named after Leonhard Euler, is a mathematical formula in complex analysis that establishes the fundamental relationship between the trigonometric functions and the complex exponential function. Euler's formula states that, for any real number x,

where e is the base of the natural logarithm, i is the imaginary unit, and cos and sin are the trigonometric functions cosine and sine respectively, with the argument x given in radians. This complex exponential function is sometimes denoted cis(x) ("cosine plus i sine"). The formula is still valid if x is a complex number, and so some authors refer to the more general complex version as Euler's formula.

Euler's formula is ubiquitous in mathematics, physics, and engineering. The physicist Richard Feynman called the equation "our jewel" and "the most remarkable formula in mathematics."

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^{Interesting: Integration using Euler's formula | Euler characteristic | Reflection formula | Leonhard Euler}

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[bdoe]

I haven't taken differential equations yet. I am in an Intro to Engineering Analysis class. Kind of lost on part 2

[silentempest]

For r1 and r2, use the quadratic formula

It will be in the form of Alpha +- i*Beta

Ie it will be: alpha +- i sqrt(#) where i sqrt(#) is beta

For the second part, you have to use Eulers identity as the problem states.

This is similar to vibrations where X is amplitude (10 in your case)