Solve (sqrt{11}+2i)(sqrt{11}-2i)

$$( \sqrt { 11 } + 2 i ) ( \sqrt { 11 } - 2 i )$$

Evaluate

$$15$$

Solution Steps

Apply the distributive property by multiplying each term of \sqrt{11}+2i by each term of \sqrt{11}-2i.

$$\left(\sqrt{11}\right)^{2}-2i\sqrt{11}+2i\sqrt{11}+4$$

The square of \sqrt{11} is 11.

$$11-2i\sqrt{11}+2i\sqrt{11}+4$$

Combine -2i\sqrt{11} and 2i\sqrt{11} to get 0.

$$11+4$$

Add 11 and 4 to get 15.

$$15$$

Real Part

$$15$$

Solution Steps

Apply the distributive property by multiplying each term of \sqrt{11}+2i by each term of \sqrt{11}-2i.

$$Re(\left(\sqrt{11}\right)^{2}-2i\sqrt{11}+2i\sqrt{11}+4)$$

The square of \sqrt{11} is 11.

$$Re(11-2i\sqrt{11}+2i\sqrt{11}+4)$$

Combine -2i\sqrt{11} and 2i\sqrt{11} to get 0.

$$Re(11+4)$$

Add 11 and 4 to get 15.

$$Re(15)$$

The real part of 15 is 15.

$$15$$