Evaluate
10-30i
Real Part
10
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6\times 3+6\times \left(-4i\right)-2i\times 3-2\left(-4\right)i^{2}
Multiply complex numbers 6-2i and 3-4i like you multiply binomials.
6\times 3+6\times \left(-4i\right)-2i\times 3-2\left(-4\right)\left(-1\right)
By definition, i^{2} is -1.
18-24i-6i-8
Do the multiplications.
18-8+\left(-24-6\right)i
Combine the real and imaginary parts.
10-30i
Do the additions.
Re(6\times 3+6\times \left(-4i\right)-2i\times 3-2\left(-4\right)i^{2})
Multiply complex numbers 6-2i and 3-4i like you multiply binomials.
Re(6\times 3+6\times \left(-4i\right)-2i\times 3-2\left(-4\right)\left(-1\right))
By definition, i^{2} is -1.
Re(18-24i-6i-8)
Do the multiplications in 6\times 3+6\times \left(-4i\right)-2i\times 3-2\left(-4\right)\left(-1\right).
Re(18-8+\left(-24-6\right)i)
Combine the real and imaginary parts in 18-24i-6i-8.
Re(10-30i)
Do the additions in 18-8+\left(-24-6\right)i.
10
The real part of 10-30i is 10.
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Limits
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