Evaluate
52
Real Part
52
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4\times 4+4\times \left(-6i\right)+6i\times 4+6\left(-6\right)i^{2}
Multiply complex numbers 4+6i and 4-6i like you multiply binomials.
4\times 4+4\times \left(-6i\right)+6i\times 4+6\left(-6\right)\left(-1\right)
By definition, i^{2} is -1.
16-24i+24i+36
Do the multiplications.
16+36+\left(-24+24\right)i
Combine the real and imaginary parts.
52
Do the additions.
Re(4\times 4+4\times \left(-6i\right)+6i\times 4+6\left(-6\right)i^{2})
Multiply complex numbers 4+6i and 4-6i like you multiply binomials.
Re(4\times 4+4\times \left(-6i\right)+6i\times 4+6\left(-6\right)\left(-1\right))
By definition, i^{2} is -1.
Re(16-24i+24i+36)
Do the multiplications in 4\times 4+4\times \left(-6i\right)+6i\times 4+6\left(-6\right)\left(-1\right).
Re(16+36+\left(-24+24\right)i)
Combine the real and imaginary parts in 16-24i+24i+36.
Re(52)
Do the additions in 16+36+\left(-24+24\right)i.
52
The real part of 52 is 52.
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