Evaluate
21+3i
Real Part
21
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3\times 4+3\times \left(-3i\right)+3i\times 4+3\left(-3\right)i^{2}
Multiply complex numbers 3+3i and 4-3i like you multiply binomials.
3\times 4+3\times \left(-3i\right)+3i\times 4+3\left(-3\right)\left(-1\right)
By definition, i^{2} is -1.
12-9i+12i+9
Do the multiplications.
12+9+\left(-9+12\right)i
Combine the real and imaginary parts.
21+3i
Do the additions.
Re(3\times 4+3\times \left(-3i\right)+3i\times 4+3\left(-3\right)i^{2})
Multiply complex numbers 3+3i and 4-3i like you multiply binomials.
Re(3\times 4+3\times \left(-3i\right)+3i\times 4+3\left(-3\right)\left(-1\right))
By definition, i^{2} is -1.
Re(12-9i+12i+9)
Do the multiplications in 3\times 4+3\times \left(-3i\right)+3i\times 4+3\left(-3\right)\left(-1\right).
Re(12+9+\left(-9+12\right)i)
Combine the real and imaginary parts in 12-9i+12i+9.
Re(21+3i)
Do the additions in 12+9+\left(-9+12\right)i.
21
The real part of 21+3i is 21.
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