Evaluate
1+7i
Real Part
1
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-3-\left(-4i\right)+3i-4i^{2}
Multiply complex numbers -1+i and 3-4i like you multiply binomials.
-3-\left(-4i\right)+3i-4\left(-1\right)
By definition, i^{2} is -1.
-3+4i+3i+4
Do the multiplications.
-3+4+\left(4+3\right)i
Combine the real and imaginary parts.
1+7i
Do the additions.
Re(-3-\left(-4i\right)+3i-4i^{2})
Multiply complex numbers -1+i and 3-4i like you multiply binomials.
Re(-3-\left(-4i\right)+3i-4\left(-1\right))
By definition, i^{2} is -1.
Re(-3+4i+3i+4)
Do the multiplications in -3-\left(-4i\right)+3i-4\left(-1\right).
Re(-3+4+\left(4+3\right)i)
Combine the real and imaginary parts in -3+4i+3i+4.
Re(1+7i)
Do the additions in -3+4+\left(4+3\right)i.
1
The real part of 1+7i is 1.
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Limits
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