Evaluate
15-45i
Real Part
15
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6\times 5+6\times \left(-5i\right)-3i\times 5-3\left(-5\right)i^{2}
Multiply complex numbers 6-3i and 5-5i like you multiply binomials.
6\times 5+6\times \left(-5i\right)-3i\times 5-3\left(-5\right)\left(-1\right)
By definition, i^{2} is -1.
30-30i-15i-15
Do the multiplications.
30-15+\left(-30-15\right)i
Combine the real and imaginary parts.
15-45i
Do the additions.
Re(6\times 5+6\times \left(-5i\right)-3i\times 5-3\left(-5\right)i^{2})
Multiply complex numbers 6-3i and 5-5i like you multiply binomials.
Re(6\times 5+6\times \left(-5i\right)-3i\times 5-3\left(-5\right)\left(-1\right))
By definition, i^{2} is -1.
Re(30-30i-15i-15)
Do the multiplications in 6\times 5+6\times \left(-5i\right)-3i\times 5-3\left(-5\right)\left(-1\right).
Re(30-15+\left(-30-15\right)i)
Combine the real and imaginary parts in 30-30i-15i-15.
Re(15-45i)
Do the additions in 30-15+\left(-30-15\right)i.
15
The real part of 15-45i is 15.
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