SOLUTION: multiply the following and write in standard form ( 9+ 5i) (9-5i)

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Question 1164226: multiply the following and write in standard form ( 9+ 5i) (9-5i)
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
keep in mind the following:

i = sqrt(-1)
i^2 = sqrt(-1) * sqrt(-1) = -1
i^3 = -1 * sqrt(-1)
i^4 = -1 * sqrt(-1) * sqrt(-1) = -1 * -1 = 1


your problem is (9 - 5i) * (9 + 5i)
this is equal to 9 * (9 + 5i) - 5i * (9 + 5i) which is equal to:
81 + 45i - 45i - 25i^2 which is equal to:
81 - 25i^2 which is equal to:
81 - 25 * -1 which is equal to:
81 + 25 which is equal to:
106

your answer is 106.
in standard complex number form, that would be equal to 106 + 0i.

here's a reference on complex numbers.

https://tutorial.math.lamar.edu/classes/alg/ComplexNumbers.aspx

here's another.

https://www.purplemath.com/modules/complex.htm

both references are very good and worth your while to review.

here's an online calculator you can use to check your work.

https://www.symbolab.com/solver/complex-numbers-calculator/i%5E%7B4%7D