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You can put this solution on YOUR website!
you had the right idea but you didn't go far enough.
\n" ); document.write( "you needed to multiply (2-3i) * (2-3i) to get the result of that multiplication.
\n" ); document.write( "based on the law of distributive multiplication, the result of that multiplication would be as follows:
\n" ); document.write( "(2-3i) * (2-3i) equals:
\n" ); document.write( "2*(2-3i) - 3i*(2-3i) which equals:
\n" ); document.write( "4 - 6i - 6i + 9i^2
\n" ); document.write( "subtract that from 9 - 6i and you get:
\n" ); document.write( "9 - 6i - (4 - 6i - 6i + 9i^2)
\n" ); document.write( "remove parentheses to get:
\n" ); document.write( "9 - 6i - 4 + 6i + 6i - 9i^2
\n" ); document.write( "combine like terms to get:
\n" ); document.write( "5 + 6i - 9i^2
\n" ); document.write( "since i^2 = -1, this becomes:
\n" ); document.write( "5 + 6i - 9*(-1) which becomes:
\n" ); document.write( "5 + 6i + 9
\n" ); document.write( "combine like terms to get:
\n" ); document.write( "14 + 6i
\n" ); document.write( "that's your result.
\n" ); document.write( "the properties for imaginary numbers are:
\n" ); document.write( "i = square root of (-1)
\n" ); document.write( "i^2 = -1
\n" ); document.write( "i^3 = - square root of (-1)
\n" ); document.write( "i^4 = 1
\n" ); document.write( "this pattern then repeats.
\n" ); document.write( "i^5 is the same as i
\n" ); document.write( "i^6 is the same as i^2
\n" ); document.write( "i^7 is the same as i^3
\n" ); document.write( "i^8 is the same as i^4
\n" ); document.write( "etc.
\n" ); document.write( "if you want to know the value of i^7, you would do the following.
\n" ); document.write( "divide the exponent by 4 and then your equivalent expression will be i raised to the remainder of the division.
\n" ); document.write( "example:
\n" ); document.write( "i^7 is translated to its equivalent value as follows:
\n" ); document.write( "7/4 = 1 with a remainder of 3.
\n" ); document.write( "the base value of i^7 is equal to i^3.
\n" ); document.write( "the equivalent value of i^3 is equal to - square root of (-1).
\n" ); document.write( "all the calculations are done with i remaining as a variable and then when all the calculations are completed, you translate i to it's equivalent value.
\n" ); document.write( "in some cases, you can leave the i unchanged.
\n" ); document.write( "in other cases, you will need to translate the i to it's equivalent value.
\n" ); document.write( "it depends on the requirements of the problem and what your instructor expects you to do.
\n" ); document.write( "another example of converting the i to it's equivalent value:
\n" ); document.write( "i^37 is translated to it's equivalent value as follows:
\n" ); document.write( "37/4 = 9 with a remainder of 1.
\n" ); document.write( "the base value of i^37 is equal to i^1.
\n" ); document.write( "the equivalent value of i^1 is equal to square root of (-1).
\n" ); document.write( " \n" ); document.write( "