Evaluate
30-10i
Real Part
30
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4\times 7+4i-2i\times 7-2i^{2}
Multiply complex numbers 4-2i and 7+i like you multiply binomials.
4\times 7+4i-2i\times 7-2\left(-1\right)
By definition, i^{2} is -1.
28+4i-14i+2
Do the multiplications.
28+2+\left(4-14\right)i
Combine the real and imaginary parts.
30-10i
Do the additions.
Re(4\times 7+4i-2i\times 7-2i^{2})
Multiply complex numbers 4-2i and 7+i like you multiply binomials.
Re(4\times 7+4i-2i\times 7-2\left(-1\right))
By definition, i^{2} is -1.
Re(28+4i-14i+2)
Do the multiplications in 4\times 7+4i-2i\times 7-2\left(-1\right).
Re(28+2+\left(4-14\right)i)
Combine the real and imaginary parts in 28+4i-14i+2.
Re(30-10i)
Do the additions in 28+2+\left(4-14\right)i.
30
The real part of 30-10i is 30.
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