Evaluate
30i
Real Part
0
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5\times 3+5\times \left(3i\right)+5i\times 3+5\times 3i^{2}
Multiply complex numbers 5+5i and 3+3i like you multiply binomials.
5\times 3+5\times \left(3i\right)+5i\times 3+5\times 3\left(-1\right)
By definition, i^{2} is -1.
15+15i+15i-15
Do the multiplications.
15-15+\left(15+15\right)i
Combine the real and imaginary parts.
30i
Do the additions.
Re(5\times 3+5\times \left(3i\right)+5i\times 3+5\times 3i^{2})
Multiply complex numbers 5+5i and 3+3i like you multiply binomials.
Re(5\times 3+5\times \left(3i\right)+5i\times 3+5\times 3\left(-1\right))
By definition, i^{2} is -1.
Re(15+15i+15i-15)
Do the multiplications in 5\times 3+5\times \left(3i\right)+5i\times 3+5\times 3\left(-1\right).
Re(15-15+\left(15+15\right)i)
Combine the real and imaginary parts in 15+15i+15i-15.
Re(30i)
Do the additions in 15-15+\left(15+15\right)i.
0
The real part of 30i is 0.
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