document.write( "Question 641905: What is (3i)^4 + 1 in standard form a+bi \n" ); document.write( "
Algebra.Com's Answer #403895 by DrBeeee(684)\"\" \"About 
You can put this solution on YOUR website!
Review
\n" ); document.write( "i = sqrt(-1) = 1 @ 9o degrees
\n" ); document.write( "i^2 = (sqrt(-1))^2 = -1 = 1 @ 180 degrees
\n" ); document.write( "i^3 = i*(i^2) = i*(-1) = -i = 1 @ -90 degrees
\n" ); document.write( "i^4 = i^2*i^2 = (-1)(-1) = 1 = 1 @ 0 degrees
\n" ); document.write( "Your expression
\n" ); document.write( "(1) (3i)^4 + 1 =
\n" ); document.write( "(2) (3^4)*(i)^4 + 1 =
\n" ); document.write( "(3) 81*1 + 1 =
\n" ); document.write( "(4) 82
\n" ); document.write( "Comparing (4) to the standard complex number form, we have
\n" ); document.write( "(5) a + ib
\n" ); document.write( "(6) 82 + i(0)
\n" ); document.write( "Because i^4 is real, there isn't any imaginary term in (1), and b is zero. \n" ); document.write( "
\n" );