Evaluate
48+46i
Real Part
48
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4\times 9+4\times \left(-2i\right)+6i\times 9+6\left(-2\right)i^{2}
Multiply complex numbers 4+6i and 9-2i like you multiply binomials.
4\times 9+4\times \left(-2i\right)+6i\times 9+6\left(-2\right)\left(-1\right)
By definition, i^{2} is -1.
36-8i+54i+12
Do the multiplications.
36+12+\left(-8+54\right)i
Combine the real and imaginary parts.
48+46i
Do the additions.
Re(4\times 9+4\times \left(-2i\right)+6i\times 9+6\left(-2\right)i^{2})
Multiply complex numbers 4+6i and 9-2i like you multiply binomials.
Re(4\times 9+4\times \left(-2i\right)+6i\times 9+6\left(-2\right)\left(-1\right))
By definition, i^{2} is -1.
Re(36-8i+54i+12)
Do the multiplications in 4\times 9+4\times \left(-2i\right)+6i\times 9+6\left(-2\right)\left(-1\right).
Re(36+12+\left(-8+54\right)i)
Combine the real and imaginary parts in 36-8i+54i+12.
Re(48+46i)
Do the additions in 36+12+\left(-8+54\right)i.
48
The real part of 48+46i is 48.
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