( 1 + 5 i ) ( - 2 + 3 i
Evaluate
-17-7i
Real Part
-17
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1\left(-2\right)+1\times \left(3i\right)+5i\left(-2\right)+5\times 3i^{2}
Multiply complex numbers 1+5i and -2+3i like you multiply binomials.
1\left(-2\right)+1\times \left(3i\right)+5i\left(-2\right)+5\times 3\left(-1\right)
By definition, i^{2} is -1.
-2+3i-10i-15
Do the multiplications.
-2-15+\left(3-10\right)i
Combine the real and imaginary parts.
-17-7i
Do the additions.
Re(1\left(-2\right)+1\times \left(3i\right)+5i\left(-2\right)+5\times 3i^{2})
Multiply complex numbers 1+5i and -2+3i like you multiply binomials.
Re(1\left(-2\right)+1\times \left(3i\right)+5i\left(-2\right)+5\times 3\left(-1\right))
By definition, i^{2} is -1.
Re(-2+3i-10i-15)
Do the multiplications in 1\left(-2\right)+1\times \left(3i\right)+5i\left(-2\right)+5\times 3\left(-1\right).
Re(-2-15+\left(3-10\right)i)
Combine the real and imaginary parts in -2+3i-10i-15.
Re(-17-7i)
Do the additions in -2-15+\left(3-10\right)i.
-17
The real part of -17-7i is -17.
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