Evaluate
-9-15i
Real Part
-9
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1\times 3+1\times \left(-3i\right)-4i\times 3-4\left(-3\right)i^{2}
Multiply complex numbers 1-4i and 3-3i like you multiply binomials.
1\times 3+1\times \left(-3i\right)-4i\times 3-4\left(-3\right)\left(-1\right)
By definition, i^{2} is -1.
3-3i-12i-12
Do the multiplications.
3-12+\left(-3-12\right)i
Combine the real and imaginary parts.
-9-15i
Do the additions.
Re(1\times 3+1\times \left(-3i\right)-4i\times 3-4\left(-3\right)i^{2})
Multiply complex numbers 1-4i and 3-3i like you multiply binomials.
Re(1\times 3+1\times \left(-3i\right)-4i\times 3-4\left(-3\right)\left(-1\right))
By definition, i^{2} is -1.
Re(3-3i-12i-12)
Do the multiplications in 1\times 3+1\times \left(-3i\right)-4i\times 3-4\left(-3\right)\left(-1\right).
Re(3-12+\left(-3-12\right)i)
Combine the real and imaginary parts in 3-3i-12i-12.
Re(-9-15i)
Do the additions in 3-12+\left(-3-12\right)i.
-9
The real part of -9-15i is -9.
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Limits
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