Evaluate
-267+204i
Real Part
-267
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3\left(7+\left(4+8\right)i\right)\left(8i+1\right)
Combine the real and imaginary parts in 4i+8i+7.
3\left(7+12i\right)\left(8i+1\right)
Add 4 to 8.
\left(3\times 7+3\times \left(12i\right)\right)\left(8i+1\right)
Multiply 3 times 7+12i.
\left(21+36i\right)\left(8i+1\right)
Do the multiplications.
-288+168i+\left(21+36i\right)
Use the distributive property to multiply 21+36i by 8i+1.
-288+21+\left(168+36\right)i
Combine the real and imaginary parts in numbers -288+168i and 21+36i.
-267+204i
Add -288 to 21. Add 168 to 36.
Re(3\left(7+\left(4+8\right)i\right)\left(8i+1\right))
Combine the real and imaginary parts in 4i+8i+7.
Re(3\left(7+12i\right)\left(8i+1\right))
Add 4 to 8.
Re(\left(3\times 7+3\times \left(12i\right)\right)\left(8i+1\right))
Multiply 3 times 7+12i.
Re(\left(21+36i\right)\left(8i+1\right))
Do the multiplications in 3\times 7+3\times \left(12i\right).
Re(-288+168i+\left(21+36i\right))
Use the distributive property to multiply 21+36i by 8i+1.
Re(-288+21+\left(168+36\right)i)
Combine the real and imaginary parts in numbers -288+168i and 21+36i.
Re(-267+204i)
Add -288 to 21. Add 168 to 36.
-267
The real part of -267+204i is -267.
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