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

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

Evaluate

$$\frac{31}{32}+i=0.96875+i$$

Solution Steps

Calculate 2 to the power of 2 and get 4.

$$i+\frac{\frac{1}{2}}{-4}\left(-2\right)^{-2}+\left(-\frac{1}{2}\right)^{0}$$

Express \frac{\frac{1}{2}}{-4} as a single fraction.

$$i+\frac{1}{2\left(-4\right)}\left(-2\right)^{-2}+\left(-\frac{1}{2}\right)^{0}$$

Multiply 2 and -4 to get -8.

$$i+\frac{1}{-8}\left(-2\right)^{-2}+\left(-\frac{1}{2}\right)^{0}$$

Fraction \frac{1}{-8} can be rewritten as -\frac{1}{8} by extracting the negative sign.

$$i-\frac{1}{8}\left(-2\right)^{-2}+\left(-\frac{1}{2}\right)^{0}$$

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

$$i-\frac{1}{8}\times \frac{1}{4}+\left(-\frac{1}{2}\right)^{0}$$

Multiply -\frac{1}{8} and \frac{1}{4} to get -\frac{1}{32}.

$$i-\frac{1}{32}+\left(-\frac{1}{2}\right)^{0}$$

Calculate -\frac{1}{2} to the power of 0 and get 1.

$$i-\frac{1}{32}+1$$

Do the additions.

$$\frac{31}{32}+i$$

Real Part

$$\frac{31}{32} = 0.96875$$

Solution Steps

Calculate 2 to the power of 2 and get 4.

$$Re(i+\frac{\frac{1}{2}}{-4}\left(-2\right)^{-2}+\left(-\frac{1}{2}\right)^{0})$$

Express \frac{\frac{1}{2}}{-4} as a single fraction.

$$Re(i+\frac{1}{2\left(-4\right)}\left(-2\right)^{-2}+\left(-\frac{1}{2}\right)^{0})$$

Multiply 2 and -4 to get -8.

$$Re(i+\frac{1}{-8}\left(-2\right)^{-2}+\left(-\frac{1}{2}\right)^{0})$$

Fraction \frac{1}{-8} can be rewritten as -\frac{1}{8} by extracting the negative sign.

$$Re(i-\frac{1}{8}\left(-2\right)^{-2}+\left(-\frac{1}{2}\right)^{0})$$

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

$$Re(i-\frac{1}{8}\times \frac{1}{4}+\left(-\frac{1}{2}\right)^{0})$$

Multiply -\frac{1}{8} and \frac{1}{4} to get -\frac{1}{32}.

$$Re(i-\frac{1}{32}+\left(-\frac{1}{2}\right)^{0})$$

Calculate -\frac{1}{2} to the power of 0 and get 1.

$$Re(i-\frac{1}{32}+1)$$

Do the additions in i-\frac{1}{32}+1.

$$Re(\frac{31}{32}+i)$$

The real part of \frac{31}{32}+i is \frac{31}{32}.

$$\frac{31}{32}$$