Evaluate
-16-52i
Real Part
-16
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2\times 7+2\times \left(-5i\right)-6i\times 7-6\left(-5\right)i^{2}
Multiply complex numbers 2-6i and 7-5i like you multiply binomials.
2\times 7+2\times \left(-5i\right)-6i\times 7-6\left(-5\right)\left(-1\right)
By definition, i^{2} is -1.
14-10i-42i-30
Do the multiplications.
14-30+\left(-10-42\right)i
Combine the real and imaginary parts.
-16-52i
Do the additions.
Re(2\times 7+2\times \left(-5i\right)-6i\times 7-6\left(-5\right)i^{2})
Multiply complex numbers 2-6i and 7-5i like you multiply binomials.
Re(2\times 7+2\times \left(-5i\right)-6i\times 7-6\left(-5\right)\left(-1\right))
By definition, i^{2} is -1.
Re(14-10i-42i-30)
Do the multiplications in 2\times 7+2\times \left(-5i\right)-6i\times 7-6\left(-5\right)\left(-1\right).
Re(14-30+\left(-10-42\right)i)
Combine the real and imaginary parts in 14-10i-42i-30.
Re(-16-52i)
Do the additions in 14-30+\left(-10-42\right)i.
-16
The real part of -16-52i is -16.
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