Evaluate
4i
Real Part
0
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\sqrt{3}+i+i\left(\sqrt{3}\right)^{2}-\sqrt{3}
Apply the distributive property by multiplying each term of 1+i\sqrt{3} by each term of \sqrt{3}+i.
\sqrt{3}+i+3i-\sqrt{3}
The square of \sqrt{3} is 3.
\sqrt{3}+4i-\sqrt{3}
Add i and 3i to get 4i.
4i
Combine \sqrt{3} and -\sqrt{3} to get 0.
Re(\sqrt{3}+i+i\left(\sqrt{3}\right)^{2}-\sqrt{3})
Apply the distributive property by multiplying each term of 1+i\sqrt{3} by each term of \sqrt{3}+i.
Re(\sqrt{3}+i+3i-\sqrt{3})
The square of \sqrt{3} is 3.
Re(\sqrt{3}+4i-\sqrt{3})
Add i and 3i to get 4i.
Re(4i)
Combine \sqrt{3} and -\sqrt{3} to get 0.
0
The real part of 4i is 0.
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