Complex Numbers, a+bi, can be written in Trigonometric form as r(cosθ+isinθ) where r is the square root of a2+b2. and θ is equal to tan-1(b/a). Euler’s formula states that reiθ 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)



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-1 + 0i = eiπ = 1(Cos(π)+isin(π))

Which implies that the

ln(-2) = ln(2)+ln(-1)

ln(-2) = ln(2)+ln(eiπ)

ln(-2) = ln(2)+iπlne

ln(-2) = ln(2)+iπ

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The AMATYC (American Mathematical Association of Two-Year Colleges) Math contest is a national competition open to any student who has not earned a two-year degree or higher.  Part-time students are eligible. The difficulty in this competition lies in the creativity of the questions and require only a basic understanding of Math to answer. The prize and competition are sponsored by the Math Club and we look forward to seeing everyone their! Please continue to our AMATYC Page to see practice questions and tips/tricks to be successful!