Evaluate (complex solution)
16+12i
Real Part (complex solution)
16
Evaluate
\text{Indeterminate}
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\left(2+4i\right)\left(4-\sqrt{-4}\right)
Calculate the square root of -16 and get 4i.
\left(2+4i\right)\left(4-2i\right)
Calculate the square root of -4 and get 2i.
2\times 4+2\times \left(-2i\right)+4i\times 4+4\left(-2\right)i^{2}
Multiply complex numbers 2+4i and 4-2i like you multiply binomials.
2\times 4+2\times \left(-2i\right)+4i\times 4+4\left(-2\right)\left(-1\right)
By definition, i^{2} is -1.
8-4i+16i+8
Do the multiplications.
8+8+\left(-4+16\right)i
Combine the real and imaginary parts.
16+12i
Do the additions.
Re(\left(2+4i\right)\left(4-\sqrt{-4}\right))
Calculate the square root of -16 and get 4i.
Re(\left(2+4i\right)\left(4-2i\right))
Calculate the square root of -4 and get 2i.
Re(2\times 4+2\times \left(-2i\right)+4i\times 4+4\left(-2\right)i^{2})
Multiply complex numbers 2+4i and 4-2i like you multiply binomials.
Re(2\times 4+2\times \left(-2i\right)+4i\times 4+4\left(-2\right)\left(-1\right))
By definition, i^{2} is -1.
Re(8-4i+16i+8)
Do the multiplications in 2\times 4+2\times \left(-2i\right)+4i\times 4+4\left(-2\right)\left(-1\right).
Re(8+8+\left(-4+16\right)i)
Combine the real and imaginary parts in 8-4i+16i+8.
Re(16+12i)
Do the additions in 8+8+\left(-4+16\right)i.
16
The real part of 16+12i is 16.
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