Evaluate
27-24i
Real Part
27
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6\times 2+6\times \left(-5i\right)+3i\times 2+3\left(-5\right)i^{2}
Multiply complex numbers 6+3i and 2-5i like you multiply binomials.
6\times 2+6\times \left(-5i\right)+3i\times 2+3\left(-5\right)\left(-1\right)
By definition, i^{2} is -1.
12-30i+6i+15
Do the multiplications.
12+15+\left(-30+6\right)i
Combine the real and imaginary parts.
27-24i
Do the additions.
Re(6\times 2+6\times \left(-5i\right)+3i\times 2+3\left(-5\right)i^{2})
Multiply complex numbers 6+3i and 2-5i like you multiply binomials.
Re(6\times 2+6\times \left(-5i\right)+3i\times 2+3\left(-5\right)\left(-1\right))
By definition, i^{2} is -1.
Re(12-30i+6i+15)
Do the multiplications in 6\times 2+6\times \left(-5i\right)+3i\times 2+3\left(-5\right)\left(-1\right).
Re(12+15+\left(-30+6\right)i)
Combine the real and imaginary parts in 12-30i+6i+15.
Re(27-24i)
Do the additions in 12+15+\left(-30+6\right)i.
27
The real part of 27-24i is 27.
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