Evaluate
19+33i
Real Part
19
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2\times 7+2\left(-i\right)+5i\times 7+5\left(-1\right)i^{2}
Multiply complex numbers 2+5i and 7-i like you multiply binomials.
2\times 7+2\left(-i\right)+5i\times 7+5\left(-1\right)\left(-1\right)
By definition, i^{2} is -1.
14-2i+35i+5
Do the multiplications.
14+5+\left(-2+35\right)i
Combine the real and imaginary parts.
19+33i
Do the additions.
Re(2\times 7+2\left(-i\right)+5i\times 7+5\left(-1\right)i^{2})
Multiply complex numbers 2+5i and 7-i like you multiply binomials.
Re(2\times 7+2\left(-i\right)+5i\times 7+5\left(-1\right)\left(-1\right))
By definition, i^{2} is -1.
Re(14-2i+35i+5)
Do the multiplications in 2\times 7+2\left(-i\right)+5i\times 7+5\left(-1\right)\left(-1\right).
Re(14+5+\left(-2+35\right)i)
Combine the real and imaginary parts in 14-2i+35i+5.
Re(19+33i)
Do the additions in 14+5+\left(-2+35\right)i.
19
The real part of 19+33i is 19.
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