Solve [1-1+sqrt{-1/9}divsqrt{-1}]^-1

$$[ 1 - 1 + \sqrt { - \frac { 1 } { 9 } } \div \sqrt { - 1 } ] ^ { - 1 }$$

Evaluate (complex solution)

$$3$$

Solution Steps

Subtract 1 from 1 to get 0.

$$\left(\frac{\sqrt{-\frac{1}{9}}}{\sqrt{-1}}\right)^{-1}$$

Calculate the square root of -\frac{1}{9} and get \frac{1}{3}i.

$$\left(\frac{\frac{1}{3}i}{\sqrt{-1}}\right)^{-1}$$

Calculate the square root of -1 and get i.

$$\left(\frac{\frac{1}{3}i}{i}\right)^{-1}$$

Divide \frac{1}{3}i by i to get \frac{1}{3}.

$$\left(\frac{1}{3}\right)^{-1}$$

Calculate \frac{1}{3} to the power of -1 and get 3.

$$3$$

Real Part (complex solution)

$$3$$

Solution Steps

Subtract 1 from 1 to get 0.

$$Re(\left(\frac{\sqrt{-\frac{1}{9}}}{\sqrt{-1}}\right)^{-1})$$

Calculate the square root of -\frac{1}{9} and get \frac{1}{3}i.

$$Re(\left(\frac{\frac{1}{3}i}{\sqrt{-1}}\right)^{-1})$$

Calculate the square root of -1 and get i.

$$Re(\left(\frac{\frac{1}{3}i}{i}\right)^{-1})$$

Divide \frac{1}{3}i by i to get \frac{1}{3}.

$$Re(\left(\frac{1}{3}\right)^{-1})$$

Calculate \frac{1}{3} to the power of -1 and get 3.

$$Re(3)$$

The real part of 3 is 3.

$$3$$

Evaluate

$$\text{Indeterminate}$$

Factor

$$\text{Indeterminate}$$