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