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