Multiply
(4�ã6-12�ã5)(2�ã6+6�ã5)
Would the answer be 8�ã64-72�ã25
I don�ft think I am supposed to multiply the 4 and 6 or the 2 and 6
What does the symbols mean?
they are squre root symbols
To multiply two complex numbers, you can use the distributive property of multiplication. The distributive property states that for any three numbers a, b, and c, a multiplication problem like (a + b) * c is equal to a * c + b * c.
So, let's apply this concept to multiply the given complex numbers (4�ã6-12�ã5) and (2�ã6+6�ã5):
Step 1: Distribute the first complex number (4�ã6-12�ã5) to each term of the second complex number (2�ã6+6�ã5).
Expand the real parts: (4 * 2) + (4 * 6�ã6) + (-12�ã5 * 2) + (-12�ã5 * 6�ã6)
Expand the imaginary parts: (4 * 6�ã5) + (-12�ã5 * 2) + (4 * 6�ã5 * 6�ã5) + (-12�ã5 * 6�ã5)
Step 2: Simplify each term.
Real parts:
(4 * 2) = 8
(4 * 6�ã6) = 24�ã6
(-12�ã5 * 2) = -24�ã5
(-12�ã5 * 6�ã6) = -72�ã30
Imaginary parts:
(4 * 6�ã5) = 24�ã5
(-12�ã5 * 2) = -24�ã5
(4 * 6�ã5 * 6�ã5) = 144�ã30
(-12�ã5 * 6�ã5) = -72�ã25
Step 3: Combine the real and imaginary parts.
Real part: 8 + 24�ã6 - 24�ã5 - 72�ã30
Imaginary part: 24�ã5 - 24�ã5 + 144�ã30 - 72�ã25
Step 4: Simplify further if possible.
Real part: 8 - 72�ã30 + 24�ã6 - 24�ã5
Imaginary part: 144�ã30 - 72�ã25
Therefore, we can't conclude that the answer is 8�ã64-72�ã25. Instead, the simplified answer to the multiplication problem is:
8 - 72�ã30 + 24�ã6 - 24�ã5 + 144�ã30 - 72�ã25
This expression can be further simplified if necessary.