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\left(1\times \left(10i\right)+10i^{2}\right)\sqrt{3}
Multiply 1+i times 10i.
\left(1\times \left(10i\right)+10\left(-1\right)\right)\sqrt{3}
By definition, i^{2} is -1.
\left(-10+10i\right)\sqrt{3}
Do the multiplications. Reorder the terms.