Evaluate
12-8i
Real Part
12
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2\times 1+2\times \left(-5i\right)+2i\times 1+2\left(-5\right)i^{2}
Multiply complex numbers 2+2i and 1-5i like you multiply binomials.
2\times 1+2\times \left(-5i\right)+2i\times 1+2\left(-5\right)\left(-1\right)
By definition, i^{2} is -1.
2-10i+2i+10
Do the multiplications.
2+10+\left(-10+2\right)i
Combine the real and imaginary parts.
12-8i
Do the additions.
Re(2\times 1+2\times \left(-5i\right)+2i\times 1+2\left(-5\right)i^{2})
Multiply complex numbers 2+2i and 1-5i like you multiply binomials.
Re(2\times 1+2\times \left(-5i\right)+2i\times 1+2\left(-5\right)\left(-1\right))
By definition, i^{2} is -1.
Re(2-10i+2i+10)
Do the multiplications in 2\times 1+2\times \left(-5i\right)+2i\times 1+2\left(-5\right)\left(-1\right).
Re(2+10+\left(-10+2\right)i)
Combine the real and imaginary parts in 2-10i+2i+10.
Re(12-8i)
Do the additions in 2+10+\left(-10+2\right)i.
12
The real part of 12-8i is 12.
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