Evaluate
22+7i
Real Part
22
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4\times 3+4\times \left(-2i\right)+5i\times 3+5\left(-2\right)i^{2}
Multiply complex numbers 4+5i and 3-2i like you multiply binomials.
4\times 3+4\times \left(-2i\right)+5i\times 3+5\left(-2\right)\left(-1\right)
By definition, i^{2} is -1.
12-8i+15i+10
Do the multiplications.
12+10+\left(-8+15\right)i
Combine the real and imaginary parts.
22+7i
Do the additions.
Re(4\times 3+4\times \left(-2i\right)+5i\times 3+5\left(-2\right)i^{2})
Multiply complex numbers 4+5i and 3-2i like you multiply binomials.
Re(4\times 3+4\times \left(-2i\right)+5i\times 3+5\left(-2\right)\left(-1\right))
By definition, i^{2} is -1.
Re(12-8i+15i+10)
Do the multiplications in 4\times 3+4\times \left(-2i\right)+5i\times 3+5\left(-2\right)\left(-1\right).
Re(12+10+\left(-8+15\right)i)
Combine the real and imaginary parts in 12-8i+15i+10.
Re(22+7i)
Do the additions in 12+10+\left(-8+15\right)i.
22
The real part of 22+7i is 22.
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