Evaluate
x\left(x+\left(-2+3i\right)\right)\left(x+1\right)^{2}
Expand
x^{4}+3ix^{3}+\left(-3+6i\right)x^{2}+\left(-2+3i\right)x
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\left(x+1\right)^{2}\left(x-\left(2-3i\right)\right)x
Multiply x+1 and x+1 to get \left(x+1\right)^{2}.
\left(x^{2}+2x+1\right)\left(x-\left(2-3i\right)\right)x
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+1\right)^{2}.
\left(x^{2}\left(x-\left(2-3i\right)\right)+2x\left(x-\left(2-3i\right)\right)+x-\left(2-3i\right)\right)x
Use the distributive property to multiply x^{2}+2x+1 by x-\left(2-3i\right).
\left(x-\left(2-3i\right)\right)x^{3}+2\left(x-\left(2-3i\right)\right)x^{2}+\left(x-\left(2-3i\right)\right)x
Use the distributive property to multiply x^{2}\left(x-\left(2-3i\right)\right)+2x\left(x-\left(2-3i\right)\right)+x-\left(2-3i\right) by x.
\left(x+\left(-2+3i\right)\right)x^{3}+2\left(x-\left(2-3i\right)\right)x^{2}+\left(x-\left(2-3i\right)\right)x
Multiply -1 and 2-3i to get -2+3i.
x^{4}+\left(-2+3i\right)x^{3}+2\left(x-\left(2-3i\right)\right)x^{2}+\left(x-\left(2-3i\right)\right)x
Use the distributive property to multiply x+\left(-2+3i\right) by x^{3}.
x^{4}+\left(-2+3i\right)x^{3}+2\left(x+\left(-2+3i\right)\right)x^{2}+\left(x-\left(2-3i\right)\right)x
Multiply -1 and 2-3i to get -2+3i.
x^{4}+\left(-2+3i\right)x^{3}+\left(2x+\left(-4+6i\right)\right)x^{2}+\left(x-\left(2-3i\right)\right)x
Use the distributive property to multiply 2 by x+\left(-2+3i\right).
x^{4}+\left(-2+3i\right)x^{3}+2x^{3}+\left(-4+6i\right)x^{2}+\left(x-\left(2-3i\right)\right)x
Use the distributive property to multiply 2x+\left(-4+6i\right) by x^{2}.
x^{4}+3ix^{3}+\left(-4+6i\right)x^{2}+\left(x-\left(2-3i\right)\right)x
Combine \left(-2+3i\right)x^{3} and 2x^{3} to get 3ix^{3}.
x^{4}+3ix^{3}+\left(-4+6i\right)x^{2}+\left(x+\left(-2+3i\right)\right)x
Multiply -1 and 2-3i to get -2+3i.
x^{4}+3ix^{3}+\left(-4+6i\right)x^{2}+x^{2}+\left(-2+3i\right)x
Use the distributive property to multiply x+\left(-2+3i\right) by x.
x^{4}+3ix^{3}+\left(-3+6i\right)x^{2}+\left(-2+3i\right)x
Combine \left(-4+6i\right)x^{2} and x^{2} to get \left(-3+6i\right)x^{2}.
\left(x+1\right)^{2}\left(x-\left(2-3i\right)\right)x
Multiply x+1 and x+1 to get \left(x+1\right)^{2}.
\left(x^{2}+2x+1\right)\left(x-\left(2-3i\right)\right)x
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+1\right)^{2}.
\left(x^{2}\left(x-\left(2-3i\right)\right)+2x\left(x-\left(2-3i\right)\right)+x-\left(2-3i\right)\right)x
Use the distributive property to multiply x^{2}+2x+1 by x-\left(2-3i\right).
\left(x-\left(2-3i\right)\right)x^{3}+2\left(x-\left(2-3i\right)\right)x^{2}+\left(x-\left(2-3i\right)\right)x
Use the distributive property to multiply x^{2}\left(x-\left(2-3i\right)\right)+2x\left(x-\left(2-3i\right)\right)+x-\left(2-3i\right) by x.
\left(x+\left(-2+3i\right)\right)x^{3}+2\left(x-\left(2-3i\right)\right)x^{2}+\left(x-\left(2-3i\right)\right)x
Multiply -1 and 2-3i to get -2+3i.
x^{4}+\left(-2+3i\right)x^{3}+2\left(x-\left(2-3i\right)\right)x^{2}+\left(x-\left(2-3i\right)\right)x
Use the distributive property to multiply x+\left(-2+3i\right) by x^{3}.
x^{4}+\left(-2+3i\right)x^{3}+2\left(x+\left(-2+3i\right)\right)x^{2}+\left(x-\left(2-3i\right)\right)x
Multiply -1 and 2-3i to get -2+3i.
x^{4}+\left(-2+3i\right)x^{3}+\left(2x+\left(-4+6i\right)\right)x^{2}+\left(x-\left(2-3i\right)\right)x
Use the distributive property to multiply 2 by x+\left(-2+3i\right).
x^{4}+\left(-2+3i\right)x^{3}+2x^{3}+\left(-4+6i\right)x^{2}+\left(x-\left(2-3i\right)\right)x
Use the distributive property to multiply 2x+\left(-4+6i\right) by x^{2}.
x^{4}+3ix^{3}+\left(-4+6i\right)x^{2}+\left(x-\left(2-3i\right)\right)x
Combine \left(-2+3i\right)x^{3} and 2x^{3} to get 3ix^{3}.
x^{4}+3ix^{3}+\left(-4+6i\right)x^{2}+\left(x+\left(-2+3i\right)\right)x
Multiply -1 and 2-3i to get -2+3i.
x^{4}+3ix^{3}+\left(-4+6i\right)x^{2}+x^{2}+\left(-2+3i\right)x
Use the distributive property to multiply x+\left(-2+3i\right) by x.
x^{4}+3ix^{3}+\left(-3+6i\right)x^{2}+\left(-2+3i\right)x
Combine \left(-4+6i\right)x^{2} and x^{2} to get \left(-3+6i\right)x^{2}.
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Differentiation
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Limits
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