Evaluate
1+4\sqrt{3}i\approx 1+6.92820323i
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1+4\sqrt{3}i
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4+4i\sqrt{3}-\left(\sqrt{3}\right)^{2}
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(2+i\sqrt{3}\right)^{2}.
4+4i\sqrt{3}-3
The square of \sqrt{3} is 3.
1+4i\sqrt{3}
Subtract 3 from 4 to get 1.
4+4i\sqrt{3}-\left(\sqrt{3}\right)^{2}
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(2+i\sqrt{3}\right)^{2}.
4+4i\sqrt{3}-3
The square of \sqrt{3} is 3.
1+4i\sqrt{3}
Subtract 3 from 4 to get 1.
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