Solve frac{3isqrt{1-9}(0)}{4}

$$\frac { 3 i \sqrt { 1 - 9 } ( 0 ) } { 4 }$$

Evaluate

$$0$$

Solution Steps

Subtract 9 from 1 to get -8.

$$\frac{3i\sqrt{-8}\times 0}{4}$$

Factor -8=\left(2i\right)^{2}\times 2. Rewrite the square root of the product \sqrt{\left(2i\right)^{2}\times 2} as the product of square roots \sqrt{\left(2i\right)^{2}}\sqrt{2}. Take the square root of \left(2i\right)^{2}.

$$\frac{3i\times \left(2i\right)\sqrt{2}\times 0}{4}$$

Multiply 3i and 2i to get -6.

$$\frac{-6\sqrt{2}\times 0}{4}$$

Multiply -6 and 0 to get 0.

$$\frac{0\sqrt{2}}{4}$$

Anything times zero gives zero.

$$\frac{0}{4}$$

Zero divided by any non-zero number gives zero.

$$0$$

Real Part

$$0$$

Solution Steps

Subtract 9 from 1 to get -8.

$$Re(\frac{3i\sqrt{-8}\times 0}{4})$$

Factor -8=\left(2i\right)^{2}\times 2. Rewrite the square root of the product \sqrt{\left(2i\right)^{2}\times 2} as the product of square roots \sqrt{\left(2i\right)^{2}}\sqrt{2}. Take the square root of \left(2i\right)^{2}.

$$Re(\frac{3i\times \left(2i\right)\sqrt{2}\times 0}{4})$$

Multiply 3i and 2i to get -6.

$$Re(\frac{-6\sqrt{2}\times 0}{4})$$

Multiply -6 and 0 to get 0.

$$Re(\frac{0\sqrt{2}}{4})$$

Anything times zero gives zero.

$$Re(\frac{0}{4})$$

Zero divided by any non-zero number gives zero.

$$Re(0)$$

The real part of 0 is 0.

$$0$$