Evaluate
-318+1272i
Real Part
-318
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\left(3+5i\right)\left(159+3\times \left(53i\right)\right)
Multiply 3 and 53 to get 159.
\left(3+5i\right)\left(159+159i\right)
Multiply 3 and 53i to get 159i.
3\times 159+3\times \left(159i\right)+5i\times 159+5\times 159i^{2}
Multiply complex numbers 3+5i and 159+159i like you multiply binomials.
3\times 159+3\times \left(159i\right)+5i\times 159+5\times 159\left(-1\right)
By definition, i^{2} is -1.
477+477i+795i-795
Do the multiplications.
477-795+\left(477+795\right)i
Combine the real and imaginary parts.
-318+1272i
Do the additions.
Re(\left(3+5i\right)\left(159+3\times \left(53i\right)\right))
Multiply 3 and 53 to get 159.
Re(\left(3+5i\right)\left(159+159i\right))
Multiply 3 and 53i to get 159i.
Re(3\times 159+3\times \left(159i\right)+5i\times 159+5\times 159i^{2})
Multiply complex numbers 3+5i and 159+159i like you multiply binomials.
Re(3\times 159+3\times \left(159i\right)+5i\times 159+5\times 159\left(-1\right))
By definition, i^{2} is -1.
Re(477+477i+795i-795)
Do the multiplications in 3\times 159+3\times \left(159i\right)+5i\times 159+5\times 159\left(-1\right).
Re(477-795+\left(477+795\right)i)
Combine the real and imaginary parts in 477+477i+795i-795.
Re(-318+1272i)
Do the additions in 477-795+\left(477+795\right)i.
-318
The real part of -318+1272i is -318.
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