Evaluate
67
Real Part
67
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9\left(\sqrt{2}\right)^{2}+21i\sqrt{2}-21i\sqrt{2}+49
Apply the distributive property by multiplying each term of 3\sqrt{2}-7i by each term of 3\sqrt{2}+7i.
9\times 2+21i\sqrt{2}-21i\sqrt{2}+49
The square of \sqrt{2} is 2.
18+21i\sqrt{2}-21i\sqrt{2}+49
Multiply 9 and 2 to get 18.
18+49
Combine 21i\sqrt{2} and -21i\sqrt{2} to get 0.
67
Add 18 and 49 to get 67.
Re(9\left(\sqrt{2}\right)^{2}+21i\sqrt{2}-21i\sqrt{2}+49)
Apply the distributive property by multiplying each term of 3\sqrt{2}-7i by each term of 3\sqrt{2}+7i.
Re(9\times 2+21i\sqrt{2}-21i\sqrt{2}+49)
The square of \sqrt{2} is 2.
Re(18+21i\sqrt{2}-21i\sqrt{2}+49)
Multiply 9 and 2 to get 18.
Re(18+49)
Combine 21i\sqrt{2} and -21i\sqrt{2} to get 0.
Re(67)
Add 18 and 49 to get 67.
67
The real part of 67 is 67.
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