Evaluate
29
Real Part
29
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2\times 2+2\times \left(-5i\right)+5i\times 2+5\left(-5\right)i^{2}
Multiply complex numbers 2+5i and 2-5i like you multiply binomials.
2\times 2+2\times \left(-5i\right)+5i\times 2+5\left(-5\right)\left(-1\right)
By definition, i^{2} is -1.
4-10i+10i+25
Do the multiplications.
4+25+\left(-10+10\right)i
Combine the real and imaginary parts.
29
Do the additions.
Re(2\times 2+2\times \left(-5i\right)+5i\times 2+5\left(-5\right)i^{2})
Multiply complex numbers 2+5i and 2-5i like you multiply binomials.
Re(2\times 2+2\times \left(-5i\right)+5i\times 2+5\left(-5\right)\left(-1\right))
By definition, i^{2} is -1.
Re(4-10i+10i+25)
Do the multiplications in 2\times 2+2\times \left(-5i\right)+5i\times 2+5\left(-5\right)\left(-1\right).
Re(4+25+\left(-10+10\right)i)
Combine the real and imaginary parts in 4-10i+10i+25.
Re(29)
Do the additions in 4+25+\left(-10+10\right)i.
29
The real part of 29 is 29.
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