Solve (isqrt{2}-1)(2isqrt{2}+3)

$$( i \sqrt { 2 } - 1 ) ( 2 i \sqrt { 2 } + 3 )$$

Evaluate

$$-7+\sqrt{2}i\approx -7+1.414213562i$$

Solution Steps

Apply the distributive property by multiplying each term of i\sqrt{2}-1 by each term of 2i\sqrt{2}+3.

$$-2\left(\sqrt{2}\right)^{2}+3i\sqrt{2}-2i\sqrt{2}-3$$

The square of \sqrt{2} is 2.

$$-2\times 2+3i\sqrt{2}-2i\sqrt{2}-3$$

Multiply -2 and 2 to get -4.

$$-4+3i\sqrt{2}-2i\sqrt{2}-3$$

Combine 3i\sqrt{2} and -2i\sqrt{2} to get i\sqrt{2}.

$$-4+i\sqrt{2}-3$$

Subtract 3 from -4 to get -7.

$$-7+i\sqrt{2}$$

Real Part

$$-7$$