Solve (isqrt{-162})(sqrt{-108})

$$( i \sqrt { - 162 } ) ( \sqrt { - 108 } )$$

Evaluate

$$-54\sqrt{6}i\approx -0-132.27244611i$$

Solution Steps

Factor -162=\left(9i\right)^{2}\times 2. Rewrite the square root of the product \sqrt{\left(9i\right)^{2}\times 2} as the product of square roots \sqrt{\left(9i\right)^{2}}\sqrt{2}. Take the square root of \left(9i\right)^{2}.

$$i\times \left(9i\right)\sqrt{2}\sqrt{-108}$$

Multiply i and 9i to get -9.

$$-9\sqrt{2}\sqrt{-108}$$

Factor -108=\left(6i\right)^{2}\times 3. Rewrite the square root of the product \sqrt{\left(6i\right)^{2}\times 3} as the product of square roots \sqrt{\left(6i\right)^{2}}\sqrt{3}. Take the square root of \left(6i\right)^{2}.

$$-9\sqrt{2}\times \left(6i\right)\sqrt{3}$$

Multiply -9 and 6i to get -54i.

$$-54i\sqrt{2}\sqrt{3}$$

To multiply \sqrt{2} and \sqrt{3}, multiply the numbers under the square root.

$$-54i\sqrt{6}$$

Real Part

$$0$$