Evaluate
15+45i
Real Part
15
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-4\times 3-4\times \left(-9i\right)+3i\times 3+3\left(-9\right)i^{2}
Multiply complex numbers -4+3i and 3-9i like you multiply binomials.
-4\times 3-4\times \left(-9i\right)+3i\times 3+3\left(-9\right)\left(-1\right)
By definition, i^{2} is -1.
-12+36i+9i+27
Do the multiplications.
-12+27+\left(36+9\right)i
Combine the real and imaginary parts.
15+45i
Do the additions.
Re(-4\times 3-4\times \left(-9i\right)+3i\times 3+3\left(-9\right)i^{2})
Multiply complex numbers -4+3i and 3-9i like you multiply binomials.
Re(-4\times 3-4\times \left(-9i\right)+3i\times 3+3\left(-9\right)\left(-1\right))
By definition, i^{2} is -1.
Re(-12+36i+9i+27)
Do the multiplications in -4\times 3-4\times \left(-9i\right)+3i\times 3+3\left(-9\right)\left(-1\right).
Re(-12+27+\left(36+9\right)i)
Combine the real and imaginary parts in -12+36i+9i+27.
Re(15+45i)
Do the additions in -12+27+\left(36+9\right)i.
15
The real part of 15+45i is 15.
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