Multiply. Show your work.
(Type your answer in the form a+bi.)
(√3 + 6i)(√3 - 6i)
To multiply these complex numbers, we can use the FOIL method:
(√3 + 6i)(√3 - 6i)
= √3 * √3 + √3 * (-6i) + 6i * √3 + 6i * (-6i)
= 3 - 6√3i + 6√3i - 36i^2
Remember that i^2 is equal to -1:
= 3 - 6√3i + 6√3i - 36(-1)
= 3 + 36 + 12√3i - 6√3i
Combine like terms:
= 39 + 6√3i - 6√3i
= 39
Therefore, the result of (√3 + 6i)(√3 - 6i) is 39.