Evaluate
23-14i
Real Part
23
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4\times 2+4\times \left(-5i\right)+3i\times 2+3\left(-5\right)i^{2}
Multiply complex numbers 4+3i and 2-5i like you multiply binomials.
4\times 2+4\times \left(-5i\right)+3i\times 2+3\left(-5\right)\left(-1\right)
By definition, i^{2} is -1.
8-20i+6i+15
Do the multiplications.
8+15+\left(-20+6\right)i
Combine the real and imaginary parts.
23-14i
Do the additions.
Re(4\times 2+4\times \left(-5i\right)+3i\times 2+3\left(-5\right)i^{2})
Multiply complex numbers 4+3i and 2-5i like you multiply binomials.
Re(4\times 2+4\times \left(-5i\right)+3i\times 2+3\left(-5\right)\left(-1\right))
By definition, i^{2} is -1.
Re(8-20i+6i+15)
Do the multiplications in 4\times 2+4\times \left(-5i\right)+3i\times 2+3\left(-5\right)\left(-1\right).
Re(8+15+\left(-20+6\right)i)
Combine the real and imaginary parts in 8-20i+6i+15.
Re(23-14i)
Do the additions in 8+15+\left(-20+6\right)i.
23
The real part of 23-14i is 23.
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