Evaluate
-31-38i
Real Part
-31
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1\left(-7\right)+1\times \left(4i\right)+6i\left(-7\right)+6\times 4i^{2}
Multiply complex numbers 1+6i and -7+4i like you multiply binomials.
1\left(-7\right)+1\times \left(4i\right)+6i\left(-7\right)+6\times 4\left(-1\right)
By definition, i^{2} is -1.
-7+4i-42i-24
Do the multiplications.
-7-24+\left(4-42\right)i
Combine the real and imaginary parts.
-31-38i
Do the additions.
Re(1\left(-7\right)+1\times \left(4i\right)+6i\left(-7\right)+6\times 4i^{2})
Multiply complex numbers 1+6i and -7+4i like you multiply binomials.
Re(1\left(-7\right)+1\times \left(4i\right)+6i\left(-7\right)+6\times 4\left(-1\right))
By definition, i^{2} is -1.
Re(-7+4i-42i-24)
Do the multiplications in 1\left(-7\right)+1\times \left(4i\right)+6i\left(-7\right)+6\times 4\left(-1\right).
Re(-7-24+\left(4-42\right)i)
Combine the real and imaginary parts in -7+4i-42i-24.
Re(-31-38i)
Do the additions in -7-24+\left(4-42\right)i.
-31
The real part of -31-38i is -31.
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