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