Evaluate
32+8i
Real Part
32
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3\times 4+3\times \left(-4i\right)+5i\times 4+5\left(-4\right)i^{2}
Multiply complex numbers 3+5i and 4-4i like you multiply binomials.
3\times 4+3\times \left(-4i\right)+5i\times 4+5\left(-4\right)\left(-1\right)
By definition, i^{2} is -1.
12-12i+20i+20
Do the multiplications.
12+20+\left(-12+20\right)i
Combine the real and imaginary parts.
32+8i
Do the additions.
Re(3\times 4+3\times \left(-4i\right)+5i\times 4+5\left(-4\right)i^{2})
Multiply complex numbers 3+5i and 4-4i like you multiply binomials.
Re(3\times 4+3\times \left(-4i\right)+5i\times 4+5\left(-4\right)\left(-1\right))
By definition, i^{2} is -1.
Re(12-12i+20i+20)
Do the multiplications in 3\times 4+3\times \left(-4i\right)+5i\times 4+5\left(-4\right)\left(-1\right).
Re(12+20+\left(-12+20\right)i)
Combine the real and imaginary parts in 12-12i+20i+20.
Re(32+8i)
Do the additions in 12+20+\left(-12+20\right)i.
32
The real part of 32+8i is 32.
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