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