Evaluate
19+67i
Real Part
19
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1\left(-9\right)+1\times \left(4i\right)-7i\left(-9\right)-7\times 4i^{2}
Multiply complex numbers 1-7i and -9+4i like you multiply binomials.
1\left(-9\right)+1\times \left(4i\right)-7i\left(-9\right)-7\times 4\left(-1\right)
By definition, i^{2} is -1.
-9+4i+63i+28
Do the multiplications.
-9+28+\left(4+63\right)i
Combine the real and imaginary parts.
19+67i
Do the additions.
Re(1\left(-9\right)+1\times \left(4i\right)-7i\left(-9\right)-7\times 4i^{2})
Multiply complex numbers 1-7i and -9+4i like you multiply binomials.
Re(1\left(-9\right)+1\times \left(4i\right)-7i\left(-9\right)-7\times 4\left(-1\right))
By definition, i^{2} is -1.
Re(-9+4i+63i+28)
Do the multiplications in 1\left(-9\right)+1\times \left(4i\right)-7i\left(-9\right)-7\times 4\left(-1\right).
Re(-9+28+\left(4+63\right)i)
Combine the real and imaginary parts in -9+4i+63i+28.
Re(19+67i)
Do the additions in -9+28+\left(4+63\right)i.
19
The real part of 19+67i is 19.
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