Evaluate
-60+25i
Real Part
-60
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\left(5\left(-2\right)+5\times \left(3i\right)\right)\left(3+2i\right)
Multiply 5 times -2+3i.
\left(-10+15i\right)\left(3+2i\right)
Do the multiplications.
-10\times 3-10\times \left(2i\right)+15i\times 3+15\times 2i^{2}
Multiply complex numbers -10+15i and 3+2i like you multiply binomials.
-10\times 3-10\times \left(2i\right)+15i\times 3+15\times 2\left(-1\right)
By definition, i^{2} is -1.
-30-20i+45i-30
Do the multiplications.
-30-30+\left(-20+45\right)i
Combine the real and imaginary parts.
-60+25i
Do the additions.
Re(\left(5\left(-2\right)+5\times \left(3i\right)\right)\left(3+2i\right))
Multiply 5 times -2+3i.
Re(\left(-10+15i\right)\left(3+2i\right))
Do the multiplications in 5\left(-2\right)+5\times \left(3i\right).
Re(-10\times 3-10\times \left(2i\right)+15i\times 3+15\times 2i^{2})
Multiply complex numbers -10+15i and 3+2i like you multiply binomials.
Re(-10\times 3-10\times \left(2i\right)+15i\times 3+15\times 2\left(-1\right))
By definition, i^{2} is -1.
Re(-30-20i+45i-30)
Do the multiplications in -10\times 3-10\times \left(2i\right)+15i\times 3+15\times 2\left(-1\right).
Re(-30-30+\left(-20+45\right)i)
Combine the real and imaginary parts in -30-20i+45i-30.
Re(-60+25i)
Do the additions in -30-30+\left(-20+45\right)i.
-60
The real part of -60+25i is -60.
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Limits
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