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