Evaluate
50
Real Part
50
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5\times 5+5\times \left(-5i\right)+5i\times 5+5\left(-5\right)i^{2}
Multiply complex numbers 5+5i and 5-5i like you multiply binomials.
5\times 5+5\times \left(-5i\right)+5i\times 5+5\left(-5\right)\left(-1\right)
By definition, i^{2} is -1.
25-25i+25i+25
Do the multiplications.
25+25+\left(-25+25\right)i
Combine the real and imaginary parts.
50
Do the additions.
Re(5\times 5+5\times \left(-5i\right)+5i\times 5+5\left(-5\right)i^{2})
Multiply complex numbers 5+5i and 5-5i like you multiply binomials.
Re(5\times 5+5\times \left(-5i\right)+5i\times 5+5\left(-5\right)\left(-1\right))
By definition, i^{2} is -1.
Re(25-25i+25i+25)
Do the multiplications in 5\times 5+5\times \left(-5i\right)+5i\times 5+5\left(-5\right)\left(-1\right).
Re(25+25+\left(-25+25\right)i)
Combine the real and imaginary parts in 25-25i+25i+25.
Re(50)
Do the additions in 25+25+\left(-25+25\right)i.
50
The real part of 50 is 50.
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