Evaluate
-12+39i
Real Part
-12
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6\left(-3\right)+6\times \left(6i\right)-i\left(-3\right)-6i^{2}
Multiply complex numbers 6-i and -3+6i like you multiply binomials.
6\left(-3\right)+6\times \left(6i\right)-i\left(-3\right)-6\left(-1\right)
By definition, i^{2} is -1.
-18+36i+3i+6
Do the multiplications.
-18+6+\left(36+3\right)i
Combine the real and imaginary parts.
-12+39i
Do the additions.
Re(6\left(-3\right)+6\times \left(6i\right)-i\left(-3\right)-6i^{2})
Multiply complex numbers 6-i and -3+6i like you multiply binomials.
Re(6\left(-3\right)+6\times \left(6i\right)-i\left(-3\right)-6\left(-1\right))
By definition, i^{2} is -1.
Re(-18+36i+3i+6)
Do the multiplications in 6\left(-3\right)+6\times \left(6i\right)-i\left(-3\right)-6\left(-1\right).
Re(-18+6+\left(36+3\right)i)
Combine the real and imaginary parts in -18+36i+3i+6.
Re(-12+39i)
Do the additions in -18+6+\left(36+3\right)i.
-12
The real part of -12+39i is -12.
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