Evaluate
53
Real Part
53
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2\times 2+2\times \left(-7i\right)+7i\times 2+7\left(-7\right)i^{2}
Multiply complex numbers 2+7i and 2-7i like you multiply binomials.
2\times 2+2\times \left(-7i\right)+7i\times 2+7\left(-7\right)\left(-1\right)
By definition, i^{2} is -1.
4-14i+14i+49
Do the multiplications.
4+49+\left(-14+14\right)i
Combine the real and imaginary parts.
53
Do the additions.
Re(2\times 2+2\times \left(-7i\right)+7i\times 2+7\left(-7\right)i^{2})
Multiply complex numbers 2+7i and 2-7i like you multiply binomials.
Re(2\times 2+2\times \left(-7i\right)+7i\times 2+7\left(-7\right)\left(-1\right))
By definition, i^{2} is -1.
Re(4-14i+14i+49)
Do the multiplications in 2\times 2+2\times \left(-7i\right)+7i\times 2+7\left(-7\right)\left(-1\right).
Re(4+49+\left(-14+14\right)i)
Combine the real and imaginary parts in 4-14i+14i+49.
Re(53)
Do the additions in 4+49+\left(-14+14\right)i.
53
The real part of 53 is 53.
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