Evaluate
-9+43i
Real Part
-9
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1\times 12+1\times \left(7i\right)+3i\times 12+3\times 7i^{2}
Multiply complex numbers 1+3i and 12+7i like you multiply binomials.
1\times 12+1\times \left(7i\right)+3i\times 12+3\times 7\left(-1\right)
By definition, i^{2} is -1.
12+7i+36i-21
Do the multiplications.
12-21+\left(7+36\right)i
Combine the real and imaginary parts.
-9+43i
Do the additions.
Re(1\times 12+1\times \left(7i\right)+3i\times 12+3\times 7i^{2})
Multiply complex numbers 1+3i and 12+7i like you multiply binomials.
Re(1\times 12+1\times \left(7i\right)+3i\times 12+3\times 7\left(-1\right))
By definition, i^{2} is -1.
Re(12+7i+36i-21)
Do the multiplications in 1\times 12+1\times \left(7i\right)+3i\times 12+3\times 7\left(-1\right).
Re(12-21+\left(7+36\right)i)
Combine the real and imaginary parts in 12+7i+36i-21.
Re(-9+43i)
Do the additions in 12-21+\left(7+36\right)i.
-9
The real part of -9+43i is -9.
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