Solve i^-1-3*(-3)^-2+(-1/9)^0/2^-2-1

$$\frac { i ^ { - 1 } - 3 \times ( - 3 ) ^ { - 2 } + ( - \frac { 1 } { 9 } ) ^ { 0 } } { 2 ^ { - 2 } - 1 }$$

Evaluate

$$-\frac{8}{9}+\frac{4}{3}i\approx -0.888888889+1.333333333i$$

Solution Steps

Calculate i to the power of -1 and get -i.

$$\frac{-i-3\left(-3\right)^{-2}+\left(-\frac{1}{9}\right)^{0}}{2^{-2}-1}$$

Calculate -3 to the power of -2 and get \frac{1}{9}.

$$\frac{-i-3\times \frac{1}{9}+\left(-\frac{1}{9}\right)^{0}}{2^{-2}-1}$$

Multiply 3 and \frac{1}{9} to get \frac{1}{3}.

$$\frac{-i-\frac{1}{3}+\left(-\frac{1}{9}\right)^{0}}{2^{-2}-1}$$

Calculate -\frac{1}{9} to the power of 0 and get 1.

$$\frac{-i-\frac{1}{3}+1}{2^{-2}-1}$$

Do the additions in -i-\frac{1}{3}+1.

$$\frac{\frac{2}{3}-i}{2^{-2}-1}$$

Calculate 2 to the power of -2 and get \frac{1}{4}.

$$\frac{\frac{2}{3}-i}{\frac{1}{4}-1}$$

Subtract 1 from \frac{1}{4} to get -\frac{3}{4}.

$$\frac{\frac{2}{3}-i}{-\frac{3}{4}}$$

Divide \frac{2}{3}-i by -\frac{3}{4} by multiplying \frac{2}{3}-i by the reciprocal of -\frac{3}{4}.

$$\left(\frac{2}{3}-i\right)\left(-\frac{4}{3}\right)$$

Multiply \frac{2}{3}-i and -\frac{4}{3} to get -\frac{8}{9}+\frac{4}{3}i.

$$-\frac{8}{9}+\frac{4}{3}i$$

Real Part

$$-\frac{8}{9} = -0.8888888888888888$$

Solution Steps

Calculate i to the power of -1 and get -i.

$$Re(\frac{-i-3\left(-3\right)^{-2}+\left(-\frac{1}{9}\right)^{0}}{2^{-2}-1})$$

Calculate -3 to the power of -2 and get \frac{1}{9}.

$$Re(\frac{-i-3\times \frac{1}{9}+\left(-\frac{1}{9}\right)^{0}}{2^{-2}-1})$$

Multiply 3 and \frac{1}{9} to get \frac{1}{3}.

$$Re(\frac{-i-\frac{1}{3}+\left(-\frac{1}{9}\right)^{0}}{2^{-2}-1})$$

Calculate -\frac{1}{9} to the power of 0 and get 1.

$$Re(\frac{-i-\frac{1}{3}+1}{2^{-2}-1})$$

Do the additions in -i-\frac{1}{3}+1.

$$Re(\frac{\frac{2}{3}-i}{2^{-2}-1})$$

Calculate 2 to the power of -2 and get \frac{1}{4}.

$$Re(\frac{\frac{2}{3}-i}{\frac{1}{4}-1})$$

Subtract 1 from \frac{1}{4} to get -\frac{3}{4}.

$$Re(\frac{\frac{2}{3}-i}{-\frac{3}{4}})$$

Divide \frac{2}{3}-i by -\frac{3}{4} by multiplying \frac{2}{3}-i by the reciprocal of -\frac{3}{4}.

$$Re(\left(\frac{2}{3}-i\right)\left(-\frac{4}{3}\right))$$

Multiply \frac{2}{3}-i and -\frac{4}{3} to get -\frac{8}{9}+\frac{4}{3}i.

$$Re(-\frac{8}{9}+\frac{4}{3}i)$$

The real part of -\frac{8}{9}+\frac{4}{3}i is -\frac{8}{9}.

$$-\frac{8}{9}$$