Evaluate
23-15i
Real Part
23
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7\times 2+7\times \left(-3i\right)+3i\times 2+3\left(-3\right)i^{2}
Multiply complex numbers 7+3i and 2-3i like you multiply binomials.
7\times 2+7\times \left(-3i\right)+3i\times 2+3\left(-3\right)\left(-1\right)
By definition, i^{2} is -1.
14-21i+6i+9
Do the multiplications.
14+9+\left(-21+6\right)i
Combine the real and imaginary parts.
23-15i
Do the additions.
Re(7\times 2+7\times \left(-3i\right)+3i\times 2+3\left(-3\right)i^{2})
Multiply complex numbers 7+3i and 2-3i like you multiply binomials.
Re(7\times 2+7\times \left(-3i\right)+3i\times 2+3\left(-3\right)\left(-1\right))
By definition, i^{2} is -1.
Re(14-21i+6i+9)
Do the multiplications in 7\times 2+7\times \left(-3i\right)+3i\times 2+3\left(-3\right)\left(-1\right).
Re(14+9+\left(-21+6\right)i)
Combine the real and imaginary parts in 14-21i+6i+9.
Re(23-15i)
Do the additions in 14+9+\left(-21+6\right)i.
23
The real part of 23-15i is 23.
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