Evaluate
51-17i
Real Part
51
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7\times 3+7\times \left(-5i\right)+6i\times 3+6\left(-5\right)i^{2}
Multiply complex numbers 7+6i and 3-5i like you multiply binomials.
7\times 3+7\times \left(-5i\right)+6i\times 3+6\left(-5\right)\left(-1\right)
By definition, i^{2} is -1.
21-35i+18i+30
Do the multiplications.
21+30+\left(-35+18\right)i
Combine the real and imaginary parts.
51-17i
Do the additions.
Re(7\times 3+7\times \left(-5i\right)+6i\times 3+6\left(-5\right)i^{2})
Multiply complex numbers 7+6i and 3-5i like you multiply binomials.
Re(7\times 3+7\times \left(-5i\right)+6i\times 3+6\left(-5\right)\left(-1\right))
By definition, i^{2} is -1.
Re(21-35i+18i+30)
Do the multiplications in 7\times 3+7\times \left(-5i\right)+6i\times 3+6\left(-5\right)\left(-1\right).
Re(21+30+\left(-35+18\right)i)
Combine the real and imaginary parts in 21-35i+18i+30.
Re(51-17i)
Do the additions in 21+30+\left(-35+18\right)i.
51
The real part of 51-17i is 51.
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