Evaluate
2-86i
Real Part
2
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6\times 7+6\times \left(-5i\right)-8i\times 7-8\left(-5\right)i^{2}
Multiply complex numbers 6-8i and 7-5i like you multiply binomials.
6\times 7+6\times \left(-5i\right)-8i\times 7-8\left(-5\right)\left(-1\right)
By definition, i^{2} is -1.
42-30i-56i-40
Do the multiplications.
42-40+\left(-30-56\right)i
Combine the real and imaginary parts.
2-86i
Do the additions.
Re(6\times 7+6\times \left(-5i\right)-8i\times 7-8\left(-5\right)i^{2})
Multiply complex numbers 6-8i and 7-5i like you multiply binomials.
Re(6\times 7+6\times \left(-5i\right)-8i\times 7-8\left(-5\right)\left(-1\right))
By definition, i^{2} is -1.
Re(42-30i-56i-40)
Do the multiplications in 6\times 7+6\times \left(-5i\right)-8i\times 7-8\left(-5\right)\left(-1\right).
Re(42-40+\left(-30-56\right)i)
Combine the real and imaginary parts in 42-30i-56i-40.
Re(2-86i)
Do the additions in 42-40+\left(-30-56\right)i.
2
The real part of 2-86i is 2.
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