Solve i+30/7:1-1/21+2^-1-2^2

$$i + \frac { 30 } { 7 } : 1 - \frac { 1 } { 2 } 1 + 2 ^ { - 1 } - 2 ^ { 2 }$$

Evaluate

$$\frac{2}{7}+i\approx 0.285714286+i$$

Solution Steps

Anything divided by one gives itself.

$$i+\frac{30}{7}-\frac{1}{2}\times 1+2^{-1}-2^{2}$$

Multiply \frac{1}{2} and 1 to get \frac{1}{2}.

$$i+\frac{30}{7}-\frac{1}{2}+2^{-1}-2^{2}$$

Do the additions in i+\frac{30}{7}-\frac{1}{2}.

$$\frac{53}{14}+i+2^{-1}-2^{2}$$

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

$$\frac{53}{14}+i+\frac{1}{2}-2^{2}$$

Do the additions in \frac{53}{14}+i+\frac{1}{2}.

$$\frac{30}{7}+i-2^{2}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{30}{7}+i-4$$

Subtract 4 from \frac{30}{7}+i to get \frac{2}{7}+i.

$$\frac{2}{7}+i$$

Real Part

$$\frac{2}{7} = 0.2857142857142857$$

Solution Steps

Anything divided by one gives itself.

$$Re(i+\frac{30}{7}-\frac{1}{2}\times 1+2^{-1}-2^{2})$$

Multiply \frac{1}{2} and 1 to get \frac{1}{2}.

$$Re(i+\frac{30}{7}-\frac{1}{2}+2^{-1}-2^{2})$$

Do the additions in i+\frac{30}{7}-\frac{1}{2}.

$$Re(\frac{53}{14}+i+2^{-1}-2^{2})$$

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

$$Re(\frac{53}{14}+i+\frac{1}{2}-2^{2})$$

Do the additions in \frac{53}{14}+i+\frac{1}{2}.

$$Re(\frac{30}{7}+i-2^{2})$$

Calculate 2 to the power of 2 and get 4.

$$Re(\frac{30}{7}+i-4)$$

Subtract 4 from \frac{30}{7}+i to get \frac{2}{7}+i.

$$Re(\frac{2}{7}+i)$$

The real part of \frac{2}{7}+i is \frac{2}{7}.

$$\frac{2}{7}$$