Evaluate
46-4i
Real Part
46
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4\times 4+4\times \left(-6i\right)+5i\times 4+5\left(-6\right)i^{2}
Multiply complex numbers 4+5i and 4-6i like you multiply binomials.
4\times 4+4\times \left(-6i\right)+5i\times 4+5\left(-6\right)\left(-1\right)
By definition, i^{2} is -1.
16-24i+20i+30
Do the multiplications.
16+30+\left(-24+20\right)i
Combine the real and imaginary parts.
46-4i
Do the additions.
Re(4\times 4+4\times \left(-6i\right)+5i\times 4+5\left(-6\right)i^{2})
Multiply complex numbers 4+5i and 4-6i like you multiply binomials.
Re(4\times 4+4\times \left(-6i\right)+5i\times 4+5\left(-6\right)\left(-1\right))
By definition, i^{2} is -1.
Re(16-24i+20i+30)
Do the multiplications in 4\times 4+4\times \left(-6i\right)+5i\times 4+5\left(-6\right)\left(-1\right).
Re(16+30+\left(-24+20\right)i)
Combine the real and imaginary parts in 16-24i+20i+30.
Re(46-4i)
Do the additions in 16+30+\left(-24+20\right)i.
46
The real part of 46-4i is 46.
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Limits
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