Evaluate
-31+29i
Real Part
-31
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7\left(-3\right)+7\times \left(5i\right)+2i\left(-3\right)+2\times 5i^{2}
Multiply complex numbers 7+2i and -3+5i like you multiply binomials.
7\left(-3\right)+7\times \left(5i\right)+2i\left(-3\right)+2\times 5\left(-1\right)
By definition, i^{2} is -1.
-21+35i-6i-10
Do the multiplications.
-21-10+\left(35-6\right)i
Combine the real and imaginary parts.
-31+29i
Do the additions.
Re(7\left(-3\right)+7\times \left(5i\right)+2i\left(-3\right)+2\times 5i^{2})
Multiply complex numbers 7+2i and -3+5i like you multiply binomials.
Re(7\left(-3\right)+7\times \left(5i\right)+2i\left(-3\right)+2\times 5\left(-1\right))
By definition, i^{2} is -1.
Re(-21+35i-6i-10)
Do the multiplications in 7\left(-3\right)+7\times \left(5i\right)+2i\left(-3\right)+2\times 5\left(-1\right).
Re(-21-10+\left(35-6\right)i)
Combine the real and imaginary parts in -21+35i-6i-10.
Re(-31+29i)
Do the additions in -21-10+\left(35-6\right)i.
-31
The real part of -31+29i is -31.
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