Evaluate
-31+25i
Real Part
-31
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1\left(-6\right)+1\times \left(-5i\right)-5i\left(-6\right)-5\left(-5\right)i^{2}
Multiply complex numbers 1-5i and -6-5i like you multiply binomials.
1\left(-6\right)+1\times \left(-5i\right)-5i\left(-6\right)-5\left(-5\right)\left(-1\right)
By definition, i^{2} is -1.
-6-5i+30i-25
Do the multiplications.
-6-25+\left(-5+30\right)i
Combine the real and imaginary parts.
-31+25i
Do the additions.
Re(1\left(-6\right)+1\times \left(-5i\right)-5i\left(-6\right)-5\left(-5\right)i^{2})
Multiply complex numbers 1-5i and -6-5i like you multiply binomials.
Re(1\left(-6\right)+1\times \left(-5i\right)-5i\left(-6\right)-5\left(-5\right)\left(-1\right))
By definition, i^{2} is -1.
Re(-6-5i+30i-25)
Do the multiplications in 1\left(-6\right)+1\times \left(-5i\right)-5i\left(-6\right)-5\left(-5\right)\left(-1\right).
Re(-6-25+\left(-5+30\right)i)
Combine the real and imaginary parts in -6-5i+30i-25.
Re(-31+25i)
Do the additions in -6-25+\left(-5+30\right)i.
-31
The real part of -31+25i is -31.
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