Evaluate
39+43i
Real Part
39
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6i\times 7+6\left(-7\right)i^{2}+i\left(1+3i\right)
Multiply 6i times 7-7i.
6i\times 7+6\left(-7\right)\left(-1\right)+i\left(1+3i\right)
By definition, i^{2} is -1.
42+42i+i\left(1+3i\right)
Do the multiplications in 6i\times 7+6\left(-7\right)\left(-1\right). Reorder the terms.
42+42i+i+3i^{2}
Multiply i times 1+3i.
42+42i+i+3\left(-1\right)
By definition, i^{2} is -1.
42+42i+\left(-3+i\right)
Do the multiplications in i+3\left(-1\right). Reorder the terms.
42-3+\left(42+1\right)i
Combine the real and imaginary parts.
39+43i
Do the additions.
Re(6i\times 7+6\left(-7\right)i^{2}+i\left(1+3i\right))
Multiply 6i times 7-7i.
Re(6i\times 7+6\left(-7\right)\left(-1\right)+i\left(1+3i\right))
By definition, i^{2} is -1.
Re(42+42i+i\left(1+3i\right))
Do the multiplications in 6i\times 7+6\left(-7\right)\left(-1\right). Reorder the terms.
Re(42+42i+i+3i^{2})
Multiply i times 1+3i.
Re(42+42i+i+3\left(-1\right))
By definition, i^{2} is -1.
Re(42+42i+\left(-3+i\right))
Do the multiplications in i+3\left(-1\right). Reorder the terms.
Re(42-3+\left(42+1\right)i)
Combine the real and imaginary parts in 42+42i-3+i.
Re(39+43i)
Do the additions in 42-3+\left(42+1\right)i.
39
The real part of 39+43i is 39.
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