5-3�ã2 multiplied by its conjugate is...
Its supposed to be 7, but I don't get how to do this, cause now im totally confused, i thought that the conjugate came when you were to rationalize a denominator...
I did this...
15�ã2-9�ã4
15�ã2-18
Well, if you figure that 5^2 = 25, not 15, you'll be on your way
To find the product of a number and its conjugate, you need to multiply the real parts together and multiply the imaginary parts together.
In this case, you have the expression (5-3√2)(5+3√2).
Let's break it down step by step:
Step 1: Multiply the real parts together:
5 * 5 = 25.
Step 2: Multiply the imaginary parts together:
(-3√2) * (3√2) = -9 * 2 = -18.
Step 3: Combine the results from Step 1 and Step 2:
25 + (-18) = 7.
So, the product of (5-3√2)(5+3√2) is 7.
The conjugate is used in this case because multiplying by the conjugate helps eliminate the imaginary part of the expression, resulting in a real number. The conjugate is formed by changing the sign of the imaginary part.
I hope this explanation clarifies the process for you. Feel free to ask if you have any further questions!