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Complex Numbers, a+bi, can be written in Trigonometric form as r(cosθ+isinθ) where r is the square root of a^{2}+b^{2}^{.} and θ is equal to tan^{1}(b/a). Euler’s formula states that re^{i}^{θ}^{ }is another way to write r(cosθ+isinθ) with r and θ being the same. Find the complex number –1 +0i in all three forms. Then Find Ln(2). Hint: Use the Logarithmic Identiy, Ln(ab) = Ln(a) + Ln(b)

· 9/11/13 2:00pm  First Round of the Integration Bee · 9/12/13 4:00pm  First Round of the Integration Bee (Only one is required).

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Problem of the Week: ^{(Updated 8/12/13)} 
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1 + 0i = e^{i}^{π}^{ }= 1(Cos(π)+isin(π)) Which implies that the ln(2) = ln(2)+ln(1) ln(2) = ln(2)+ln(e^{i}^{π}) ln(2) = ln(2)+iπlne ln(2) = ln(2)+iπ 