Evaluate
11-10i
Real Part
11
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3\times 1+3\times \left(-4i\right)+2i\times 1+2\left(-4\right)i^{2}
Multiply complex numbers 3+2i and 1-4i like you multiply binomials.
3\times 1+3\times \left(-4i\right)+2i\times 1+2\left(-4\right)\left(-1\right)
By definition, i^{2} is -1.
3-12i+2i+8
Do the multiplications.
3+8+\left(-12+2\right)i
Combine the real and imaginary parts.
11-10i
Do the additions.
Re(3\times 1+3\times \left(-4i\right)+2i\times 1+2\left(-4\right)i^{2})
Multiply complex numbers 3+2i and 1-4i like you multiply binomials.
Re(3\times 1+3\times \left(-4i\right)+2i\times 1+2\left(-4\right)\left(-1\right))
By definition, i^{2} is -1.
Re(3-12i+2i+8)
Do the multiplications in 3\times 1+3\times \left(-4i\right)+2i\times 1+2\left(-4\right)\left(-1\right).
Re(3+8+\left(-12+2\right)i)
Combine the real and imaginary parts in 3-12i+2i+8.
Re(11-10i)
Do the additions in 3+8+\left(-12+2\right)i.
11
The real part of 11-10i is 11.
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