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Find the real part and imaginary part of (2+i)^5000\r
\n" ); document.write( "\n" ); document.write( "2 + i convert to polar form
\n" ); document.write( "x + yj = r(cos θ + j sin θ)
\n" ); document.write( "r = absolute value or modulus of the complex number
\n" ); document.write( "θ = argument of complex number
\n" ); document.write( "2 other ways of writing the polar form of a complex number:
\n" ); document.write( "1. r cis θ [means r (cos θ + j sin θ)]
\n" ); document.write( "2. r ∠ θ [means once again, r (cos θ + j sin θ)]
\n" ); document.write( "r=sqrt(x^2 + y^2)
\n" ); document.write( "r=sqrt(2^2 + 1^2)
\n" ); document.write( "r=sqrt(4 + 1)
\n" ); document.write( "r=sqrt(5)
\n" ); document.write( "α = tan^(-1) (y/x)
\n" ); document.write( "α = tan^(-1) (1/2) = 26.57 approx
\n" ); document.write( "θ = 180° - α
\n" ); document.write( "θ = 153.43
\n" ); document.write( "2+i = sqrt(5)(cos153.43 + isin153.43)
\n" ); document.write( "2+i = re^(iθ) = sqrt(5)e^(153.43i)
\n" ); document.write( "(re^(iθ))^n = r^n * e^(inθ) ( by De Moivre's Formula)
\n" ); document.write( "r^n * e^(inθ)
\n" ); document.write( "sqrt(5)^5000 * e^(i * 5000 * 153.43)
\n" ); document.write( "2.66079147267277840928321052036*10^1747 * e^(767150i)
\n" ); document.write( "2.66079147267277840928321052036*10^1747(cos767150 + isin767150)
\n" ); document.write( "2.62036807143692290977402577219*10^1747 - (4.62041590381335873388318315839*10+1746)i is your answer
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