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