Evaluate
-3+29i
Real Part
-3
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3\times 4+3\times \left(3i\right)+5i\times 4+5\times 3i^{2}
Multiply complex numbers 3+5i and 4+3i like you multiply binomials.
3\times 4+3\times \left(3i\right)+5i\times 4+5\times 3\left(-1\right)
By definition, i^{2} is -1.
12+9i+20i-15
Do the multiplications.
12-15+\left(9+20\right)i
Combine the real and imaginary parts.
-3+29i
Do the additions.
Re(3\times 4+3\times \left(3i\right)+5i\times 4+5\times 3i^{2})
Multiply complex numbers 3+5i and 4+3i like you multiply binomials.
Re(3\times 4+3\times \left(3i\right)+5i\times 4+5\times 3\left(-1\right))
By definition, i^{2} is -1.
Re(12+9i+20i-15)
Do the multiplications in 3\times 4+3\times \left(3i\right)+5i\times 4+5\times 3\left(-1\right).
Re(12-15+\left(9+20\right)i)
Combine the real and imaginary parts in 12+9i+20i-15.
Re(-3+29i)
Do the additions in 12-15+\left(9+20\right)i.
-3
The real part of -3+29i is -3.
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