Evaluate
-13+13i
Real Part
-13
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1\times 2+1\times \left(3i\right)+5i\times 2+5\times 3i^{2}
Multiply complex numbers 1+5i and 2+3i like you multiply binomials.
1\times 2+1\times \left(3i\right)+5i\times 2+5\times 3\left(-1\right)
By definition, i^{2} is -1.
2+3i+10i-15
Do the multiplications.
2-15+\left(3+10\right)i
Combine the real and imaginary parts.
-13+13i
Do the additions.
Re(1\times 2+1\times \left(3i\right)+5i\times 2+5\times 3i^{2})
Multiply complex numbers 1+5i and 2+3i like you multiply binomials.
Re(1\times 2+1\times \left(3i\right)+5i\times 2+5\times 3\left(-1\right))
By definition, i^{2} is -1.
Re(2+3i+10i-15)
Do the multiplications in 1\times 2+1\times \left(3i\right)+5i\times 2+5\times 3\left(-1\right).
Re(2-15+\left(3+10\right)i)
Combine the real and imaginary parts in 2+3i+10i-15.
Re(-13+13i)
Do the additions in 2-15+\left(3+10\right)i.
-13
The real part of -13+13i is -13.
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