Evaluate
21-i
Real Part
21
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2\times 3+2\times \left(-5i\right)+3i\times 3+3\left(-5\right)i^{2}
Multiply complex numbers 2+3i and 3-5i like you multiply binomials.
2\times 3+2\times \left(-5i\right)+3i\times 3+3\left(-5\right)\left(-1\right)
By definition, i^{2} is -1.
6-10i+9i+15
Do the multiplications.
6+15+\left(-10+9\right)i
Combine the real and imaginary parts.
21-i
Do the additions.
Re(2\times 3+2\times \left(-5i\right)+3i\times 3+3\left(-5\right)i^{2})
Multiply complex numbers 2+3i and 3-5i like you multiply binomials.
Re(2\times 3+2\times \left(-5i\right)+3i\times 3+3\left(-5\right)\left(-1\right))
By definition, i^{2} is -1.
Re(6-10i+9i+15)
Do the multiplications in 2\times 3+2\times \left(-5i\right)+3i\times 3+3\left(-5\right)\left(-1\right).
Re(6+15+\left(-10+9\right)i)
Combine the real and imaginary parts in 6-10i+9i+15.
Re(21-i)
Do the additions in 6+15+\left(-10+9\right)i.
21
The real part of 21-i is 21.
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