Evaluate
71-22i
Real Part
71
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9\times 7+9\times \left(-4i\right)+2i\times 7+2\left(-4\right)i^{2}
Multiply complex numbers 9+2i and 7-4i like you multiply binomials.
9\times 7+9\times \left(-4i\right)+2i\times 7+2\left(-4\right)\left(-1\right)
By definition, i^{2} is -1.
63-36i+14i+8
Do the multiplications.
63+8+\left(-36+14\right)i
Combine the real and imaginary parts.
71-22i
Do the additions.
Re(9\times 7+9\times \left(-4i\right)+2i\times 7+2\left(-4\right)i^{2})
Multiply complex numbers 9+2i and 7-4i like you multiply binomials.
Re(9\times 7+9\times \left(-4i\right)+2i\times 7+2\left(-4\right)\left(-1\right))
By definition, i^{2} is -1.
Re(63-36i+14i+8)
Do the multiplications in 9\times 7+9\times \left(-4i\right)+2i\times 7+2\left(-4\right)\left(-1\right).
Re(63+8+\left(-36+14\right)i)
Combine the real and imaginary parts in 63-36i+14i+8.
Re(71-22i)
Do the additions in 63+8+\left(-36+14\right)i.
71
The real part of 71-22i is 71.
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