Evaluate
38+8i
Real Part
38
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1\times 3+1\times \left(-7i\right)+5i\times 3+5\left(-7\right)i^{2}
Multiply complex numbers 1+5i and 3-7i like you multiply binomials.
1\times 3+1\times \left(-7i\right)+5i\times 3+5\left(-7\right)\left(-1\right)
By definition, i^{2} is -1.
3-7i+15i+35
Do the multiplications.
3+35+\left(-7+15\right)i
Combine the real and imaginary parts.
38+8i
Do the additions.
Re(1\times 3+1\times \left(-7i\right)+5i\times 3+5\left(-7\right)i^{2})
Multiply complex numbers 1+5i and 3-7i like you multiply binomials.
Re(1\times 3+1\times \left(-7i\right)+5i\times 3+5\left(-7\right)\left(-1\right))
By definition, i^{2} is -1.
Re(3-7i+15i+35)
Do the multiplications in 1\times 3+1\times \left(-7i\right)+5i\times 3+5\left(-7\right)\left(-1\right).
Re(3+35+\left(-7+15\right)i)
Combine the real and imaginary parts in 3-7i+15i+35.
Re(38+8i)
Do the additions in 3+35+\left(-7+15\right)i.
38
The real part of 38+8i is 38.
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