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#### Complex formulas unravelled

(7 Questions)This is an easy way to revisit the formulas known and learn new concepts.

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If n is any integer (cos\theta + i sin\theta)^{n} = cos\hspace{1mm} n\theta+ i sin \hspace{1mm} n\theta is --------- theorem. If there is an apostrophe in the name of the theorem please include that as well.

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6 across - Euler's formula evaluates to {e}^{i\pi}+1 = 0 when x= \pi . This is called Euler's --------------------------

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{e }^{ix} = cos x+ i sin x is ------------------ formula. If the name of the formula has an apostrophe please include it in the answer.

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4 down - Find the absolute value of | 3 + 4i | and enter the value in words, not numbers.

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3 across - Find the value of (-1+ √ 3i)^{12} and write it in words. If the value is 354 write it as threefivefour.

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2 down - For a real coefficient polynomial P(x) if a+bi is a root of P(x) then its complex conjugate a- bi is also a root of P(x). This theorem is called the ----------- conjugate -------- theorem. There are two blanks and hence two words in this sentence but write it as one. (7,4)

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1 down - The -------------- theorem states that if f(x) is a polynomial function degree x > 0, then f(x) has precisely f(x)= a(x-z) , (x- {z}{_2}),(x-{z}{_3})(x-{z}{_4}),......,(x-{z}{_n}) are complex zeros and a is the leading coefficient. (6,13)

by Sangeetha Pulapaka