# SOLUTION: Simplify the equation 9 - 6i - (2 - 3i)^2. i tried 9-6i-(2-3i)(2-3i)

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 Click here to see ALL problems on Polynomials-and-rational-expressions Question 588556: Simplify the equation 9 - 6i - (2 - 3i)^2. i tried 9-6i-(2-3i)(2-3i)Answer by Theo(3552)   (Show Source): You can put this solution on YOUR website!you had the right idea but you didn't go far enough. you needed to multiply (2-3i) * (2-3i) to get the result of that multiplication. based on the law of distributive multiplication, the result of that multiplication would be as follows: (2-3i) * (2-3i) equals: 2*(2-3i) - 3i*(2-3i) which equals: 4 - 6i - 6i + 9i^2 subtract that from 9 - 6i and you get: 9 - 6i - (4 - 6i - 6i + 9i^2) remove parentheses to get: 9 - 6i - 4 + 6i + 6i - 9i^2 combine like terms to get: 5 + 6i - 9i^2 since i^2 = -1, this becomes: 5 + 6i - 9*(-1) which becomes: 5 + 6i + 9 combine like terms to get: 14 + 6i that's your result. the properties for imaginary numbers are: i = square root of (-1) i^2 = -1 i^3 = - square root of (-1) i^4 = 1 this pattern then repeats. i^5 is the same as i i^6 is the same as i^2 i^7 is the same as i^3 i^8 is the same as i^4 etc. if you want to know the value of i^7, you would do the following. divide the exponent by 4 and then your equivalent expression will be i raised to the remainder of the division. example: i^7 is translated to its equivalent value as follows: 7/4 = 1 with a remainder of 3. the base value of i^7 is equal to i^3. the equivalent value of i^3 is equal to - square root of (-1). 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. in some cases, you can leave the i unchanged. in other cases, you will need to translate the i to it's equivalent value. it depends on the requirements of the problem and what your instructor expects you to do. another example of converting the i to it's equivalent value: i^37 is translated to it's equivalent value as follows: 37/4 = 9 with a remainder of 1. the base value of i^37 is equal to i^1. the equivalent value of i^1 is equal to square root of (-1).