Evaluate
11+7i
Real Part
11
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3\times 2+3\left(-i\right)+5i\times 2+5\left(-1\right)i^{2}
Multiply complex numbers 3+5i and 2-i like you multiply binomials.
3\times 2+3\left(-i\right)+5i\times 2+5\left(-1\right)\left(-1\right)
By definition, i^{2} is -1.
6-3i+10i+5
Do the multiplications.
6+5+\left(-3+10\right)i
Combine the real and imaginary parts.
11+7i
Do the additions.
Re(3\times 2+3\left(-i\right)+5i\times 2+5\left(-1\right)i^{2})
Multiply complex numbers 3+5i and 2-i like you multiply binomials.
Re(3\times 2+3\left(-i\right)+5i\times 2+5\left(-1\right)\left(-1\right))
By definition, i^{2} is -1.
Re(6-3i+10i+5)
Do the multiplications in 3\times 2+3\left(-i\right)+5i\times 2+5\left(-1\right)\left(-1\right).
Re(6+5+\left(-3+10\right)i)
Combine the real and imaginary parts in 6-3i+10i+5.
Re(11+7i)
Do the additions in 6+5+\left(-3+10\right)i.
11
The real part of 11+7i is 11.
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