Evaluate
7-45i
Real Part
7
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-6\times 3-6\times \left(5i\right)-5i\times 3-5\times 5i^{2}
Multiply complex numbers -6-5i and 3+5i like you multiply binomials.
-6\times 3-6\times \left(5i\right)-5i\times 3-5\times 5\left(-1\right)
By definition, i^{2} is -1.
-18-30i-15i+25
Do the multiplications.
-18+25+\left(-30-15\right)i
Combine the real and imaginary parts.
7-45i
Do the additions.
Re(-6\times 3-6\times \left(5i\right)-5i\times 3-5\times 5i^{2})
Multiply complex numbers -6-5i and 3+5i like you multiply binomials.
Re(-6\times 3-6\times \left(5i\right)-5i\times 3-5\times 5\left(-1\right))
By definition, i^{2} is -1.
Re(-18-30i-15i+25)
Do the multiplications in -6\times 3-6\times \left(5i\right)-5i\times 3-5\times 5\left(-1\right).
Re(-18+25+\left(-30-15\right)i)
Combine the real and imaginary parts in -18-30i-15i+25.
Re(7-45i)
Do the additions in -18+25+\left(-30-15\right)i.
7
The real part of 7-45i is 7.
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