Evaluate
29+11i
Real Part
29
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5\times 3+5\times \left(-2i\right)+7i\times 3+7\left(-2\right)i^{2}
Multiply complex numbers 5+7i and 3-2i like you multiply binomials.
5\times 3+5\times \left(-2i\right)+7i\times 3+7\left(-2\right)\left(-1\right)
By definition, i^{2} is -1.
15-10i+21i+14
Do the multiplications.
15+14+\left(-10+21\right)i
Combine the real and imaginary parts.
29+11i
Do the additions.
Re(5\times 3+5\times \left(-2i\right)+7i\times 3+7\left(-2\right)i^{2})
Multiply complex numbers 5+7i and 3-2i like you multiply binomials.
Re(5\times 3+5\times \left(-2i\right)+7i\times 3+7\left(-2\right)\left(-1\right))
By definition, i^{2} is -1.
Re(15-10i+21i+14)
Do the multiplications in 5\times 3+5\times \left(-2i\right)+7i\times 3+7\left(-2\right)\left(-1\right).
Re(15+14+\left(-10+21\right)i)
Combine the real and imaginary parts in 15-10i+21i+14.
Re(29+11i)
Do the additions in 15+14+\left(-10+21\right)i.
29
The real part of 29+11i is 29.
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