Evaluate
11+2i
Real Part
11
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4\times 2+4\left(-i\right)+3i\times 2+3\left(-1\right)i^{2}
Multiply complex numbers 4+3i and 2-i like you multiply binomials.
4\times 2+4\left(-i\right)+3i\times 2+3\left(-1\right)\left(-1\right)
By definition, i^{2} is -1.
8-4i+6i+3
Do the multiplications.
8+3+\left(-4+6\right)i
Combine the real and imaginary parts.
11+2i
Do the additions.
Re(4\times 2+4\left(-i\right)+3i\times 2+3\left(-1\right)i^{2})
Multiply complex numbers 4+3i and 2-i like you multiply binomials.
Re(4\times 2+4\left(-i\right)+3i\times 2+3\left(-1\right)\left(-1\right))
By definition, i^{2} is -1.
Re(8-4i+6i+3)
Do the multiplications in 4\times 2+4\left(-i\right)+3i\times 2+3\left(-1\right)\left(-1\right).
Re(8+3+\left(-4+6\right)i)
Combine the real and imaginary parts in 8-4i+6i+3.
Re(11+2i)
Do the additions in 8+3+\left(-4+6\right)i.
11
The real part of 11+2i is 11.
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