document.write( "Question 1007228: Use de Moivre's Theorem to find the following. Write your answer in standard form.
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Algebra.Com's Answer #623207 by rothauserc(4718) $\"\"$ $\"About$

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(1 + i)^8
\n" ); document.write( "The polar form of (1 + i) = sqrt(2) * (cos(pi/4) + (i * sin(pi/4)))
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\n" ); document.write( "complex number = (a + bi)
\n" ); document.write( "polar form = r(cos(theta) + i*sin(theta))
\n" ); document.write( "consider (1 + i)
\n" ); document.write( "r = sqrt(a + b) = sqrt(2) where a = 1 and b = 1
\n" ); document.write( "theta is pi/4 since a = 1, b=1, we have an isosceles right triangle
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\n" ); document.write( "By de Moivre's Theorem we have
\n" ); document.write( "(1 + i)^12 = [sqrt(2) * (cos(pi/4) + (i * sin(pi/4)))]^8 =
\n" ); document.write( "(sqrt(2))^8 * (cos(pi/4) + i*sin(pi/4))^8 =
\n" ); document.write( "2^4 * (cos(2pi) + i*sin(2pi))
\n" ); document.write( "16 * ( 1 + (i * 0) ) =
\n" ); document.write( "16
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