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\sqrt{-576+432i+\left(-324-432i\right)}
Use the distributive property to multiply 18+24i by 24i-18.
\sqrt{-576-324+\left(432-432\right)i}
Combine the real and imaginary parts in numbers -576+432i and -324-432i.
\sqrt{-900}
Add -576 to -324. Add 432 to -432.
30i
Calculate the square root of -900 and get 30i.
Re(\sqrt{-576+432i+\left(-324-432i\right)})
Use the distributive property to multiply 18+24i by 24i-18.
Re(\sqrt{-576-324+\left(432-432\right)i})
Combine the real and imaginary parts in numbers -576+432i and -324-432i.
Re(\sqrt{-900})
Add -576 to -324. Add 432 to -432.
Re(30i)
Calculate the square root of -900 and get 30i.
0
The real part of 30i is 0.