Evaluate
39-26i
Real Part
39
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12\times 2+12\times \left(-3i\right)+5i\times 2+5\left(-3\right)i^{2}
Multiply complex numbers 12+5i and 2-3i like you multiply binomials.
12\times 2+12\times \left(-3i\right)+5i\times 2+5\left(-3\right)\left(-1\right)
By definition, i^{2} is -1.
24-36i+10i+15
Do the multiplications.
24+15+\left(-36+10\right)i
Combine the real and imaginary parts.
39-26i
Do the additions.
Re(12\times 2+12\times \left(-3i\right)+5i\times 2+5\left(-3\right)i^{2})
Multiply complex numbers 12+5i and 2-3i like you multiply binomials.
Re(12\times 2+12\times \left(-3i\right)+5i\times 2+5\left(-3\right)\left(-1\right))
By definition, i^{2} is -1.
Re(24-36i+10i+15)
Do the multiplications in 12\times 2+12\times \left(-3i\right)+5i\times 2+5\left(-3\right)\left(-1\right).
Re(24+15+\left(-36+10\right)i)
Combine the real and imaginary parts in 24-36i+10i+15.
Re(39-26i)
Do the additions in 24+15+\left(-36+10\right)i.
39
The real part of 39-26i is 39.
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