Evaluate
11
Real Part
11
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\left(\sqrt{10}\right)^{2}-i\sqrt{10}+i\sqrt{10}+1
Apply the distributive property by multiplying each term of \sqrt{10}+i by each term of \sqrt{10}-i.
10-i\sqrt{10}+i\sqrt{10}+1
The square of \sqrt{10} is 10.
10+1
Combine -i\sqrt{10} and i\sqrt{10} to get 0.
11
Add 10 and 1 to get 11.
Re(\left(\sqrt{10}\right)^{2}-i\sqrt{10}+i\sqrt{10}+1)
Apply the distributive property by multiplying each term of \sqrt{10}+i by each term of \sqrt{10}-i.
Re(10-i\sqrt{10}+i\sqrt{10}+1)
The square of \sqrt{10} is 10.
Re(10+1)
Combine -i\sqrt{10} and i\sqrt{10} to get 0.
Re(11)
Add 10 and 1 to get 11.
11
The real part of 11 is 11.
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