Evaluate
23-7i
Real Part
23
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5\times 4+5i-3i\times 4-3i^{2}
Multiply complex numbers 5-3i and 4+i like you multiply binomials.
5\times 4+5i-3i\times 4-3\left(-1\right)
By definition, i^{2} is -1.
20+5i-12i+3
Do the multiplications.
20+3+\left(5-12\right)i
Combine the real and imaginary parts.
23-7i
Do the additions.
Re(5\times 4+5i-3i\times 4-3i^{2})
Multiply complex numbers 5-3i and 4+i like you multiply binomials.
Re(5\times 4+5i-3i\times 4-3\left(-1\right))
By definition, i^{2} is -1.
Re(20+5i-12i+3)
Do the multiplications in 5\times 4+5i-3i\times 4-3\left(-1\right).
Re(20+3+\left(5-12\right)i)
Combine the real and imaginary parts in 20+5i-12i+3.
Re(23-7i)
Do the additions in 20+3+\left(5-12\right)i.
23
The real part of 23-7i is 23.
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