Solve i+1/34(1/51-1/51-1/68)+(frac{1}{22}-frac{1}{33})div(frac{1}{33}-frac{1}{44}

$$i + \frac { 1 } { 34 } ( \frac { 1 } { 51 } - \frac { 1 } { 51 } - \frac { 1 } { 68 } ) + ( \frac { 1 } { 22 } - \frac { 1 } { 33 } ) \div ( \frac { 1 } { 33 } - \frac { 1 } { 44 }$$

Evaluate

$$\frac{4623}{2312}+i\approx 1.999567474+i$$

Solution Steps

Subtract \frac{1}{51} from \frac{1}{51} to get 0.

$$i+\frac{1}{34}\left(-\frac{1}{68}\right)+\frac{\frac{1}{22}-\frac{1}{33}}{\frac{1}{33}-\frac{1}{44}}$$

Multiply \frac{1}{34} times -\frac{1}{68} by multiplying numerator times numerator and denominator times denominator.

$$i+\frac{1\left(-1\right)}{34\times 68}+\frac{\frac{1}{22}-\frac{1}{33}}{\frac{1}{33}-\frac{1}{44}}$$

Do the multiplications in the fraction \frac{1\left(-1\right)}{34\times 68}.

$$i+\frac{-1}{2312}+\frac{\frac{1}{22}-\frac{1}{33}}{\frac{1}{33}-\frac{1}{44}}$$

Fraction \frac{-1}{2312} can be rewritten as -\frac{1}{2312} by extracting the negative sign.

$$i-\frac{1}{2312}+\frac{\frac{1}{22}-\frac{1}{33}}{\frac{1}{33}-\frac{1}{44}}$$

Least common multiple of 22 and 33 is 66. Convert \frac{1}{22} and \frac{1}{33} to fractions with denominator 66.

$$i-\frac{1}{2312}+\frac{\frac{3}{66}-\frac{2}{66}}{\frac{1}{33}-\frac{1}{44}}$$

Since \frac{3}{66} and \frac{2}{66} have the same denominator, subtract them by subtracting their numerators.

$$i-\frac{1}{2312}+\frac{\frac{3-2}{66}}{\frac{1}{33}-\frac{1}{44}}$$

Subtract 2 from 3 to get 1.

$$i-\frac{1}{2312}+\frac{\frac{1}{66}}{\frac{1}{33}-\frac{1}{44}}$$

Least common multiple of 33 and 44 is 132. Convert \frac{1}{33} and \frac{1}{44} to fractions with denominator 132.

$$i-\frac{1}{2312}+\frac{\frac{1}{66}}{\frac{4}{132}-\frac{3}{132}}$$

Since \frac{4}{132} and \frac{3}{132} have the same denominator, subtract them by subtracting their numerators.

$$i-\frac{1}{2312}+\frac{\frac{1}{66}}{\frac{4-3}{132}}$$

Subtract 3 from 4 to get 1.

$$i-\frac{1}{2312}+\frac{\frac{1}{66}}{\frac{1}{132}}$$

Divide \frac{1}{66} by \frac{1}{132} by multiplying \frac{1}{66} by the reciprocal of \frac{1}{132}.

$$i-\frac{1}{2312}+\frac{1}{66}\times 132$$

Multiply \frac{1}{66} and 132 to get \frac{132}{66}.

$$i-\frac{1}{2312}+\frac{132}{66}$$

Divide 132 by 66 to get 2.

$$i-\frac{1}{2312}+2$$

Combine the real and imaginary parts.

$$-\frac{1}{2312}+2+i$$

Add -\frac{1}{2312} to 2.

$$\frac{4623}{2312}+i$$

Real Part

$$\frac{4623}{2312} = 1\frac{2311}{2312} = 1.9995674740484428$$

Solution Steps

Subtract \frac{1}{51} from \frac{1}{51} to get 0.

$$Re(i+\frac{1}{34}\left(-\frac{1}{68}\right)+\frac{\frac{1}{22}-\frac{1}{33}}{\frac{1}{33}-\frac{1}{44}})$$

Multiply \frac{1}{34} times -\frac{1}{68} by multiplying numerator times numerator and denominator times denominator.

$$Re(i+\frac{1\left(-1\right)}{34\times 68}+\frac{\frac{1}{22}-\frac{1}{33}}{\frac{1}{33}-\frac{1}{44}})$$

Do the multiplications in the fraction \frac{1\left(-1\right)}{34\times 68}.

$$Re(i+\frac{-1}{2312}+\frac{\frac{1}{22}-\frac{1}{33}}{\frac{1}{33}-\frac{1}{44}})$$

Fraction \frac{-1}{2312} can be rewritten as -\frac{1}{2312} by extracting the negative sign.

$$Re(i-\frac{1}{2312}+\frac{\frac{1}{22}-\frac{1}{33}}{\frac{1}{33}-\frac{1}{44}})$$

Least common multiple of 22 and 33 is 66. Convert \frac{1}{22} and \frac{1}{33} to fractions with denominator 66.

$$Re(i-\frac{1}{2312}+\frac{\frac{3}{66}-\frac{2}{66}}{\frac{1}{33}-\frac{1}{44}})$$

Since \frac{3}{66} and \frac{2}{66} have the same denominator, subtract them by subtracting their numerators.

$$Re(i-\frac{1}{2312}+\frac{\frac{3-2}{66}}{\frac{1}{33}-\frac{1}{44}})$$

Subtract 2 from 3 to get 1.

$$Re(i-\frac{1}{2312}+\frac{\frac{1}{66}}{\frac{1}{33}-\frac{1}{44}})$$

Least common multiple of 33 and 44 is 132. Convert \frac{1}{33} and \frac{1}{44} to fractions with denominator 132.

$$Re(i-\frac{1}{2312}+\frac{\frac{1}{66}}{\frac{4}{132}-\frac{3}{132}})$$

Since \frac{4}{132} and \frac{3}{132} have the same denominator, subtract them by subtracting their numerators.

$$Re(i-\frac{1}{2312}+\frac{\frac{1}{66}}{\frac{4-3}{132}})$$

Subtract 3 from 4 to get 1.

$$Re(i-\frac{1}{2312}+\frac{\frac{1}{66}}{\frac{1}{132}})$$

Divide \frac{1}{66} by \frac{1}{132} by multiplying \frac{1}{66} by the reciprocal of \frac{1}{132}.

$$Re(i-\frac{1}{2312}+\frac{1}{66}\times 132)$$

Multiply \frac{1}{66} and 132 to get \frac{132}{66}.

$$Re(i-\frac{1}{2312}+\frac{132}{66})$$

Divide 132 by 66 to get 2.

$$Re(i-\frac{1}{2312}+2)$$

Combine the real and imaginary parts in i-\frac{1}{2312}+2.

$$Re(-\frac{1}{2312}+2+i)$$

Add -\frac{1}{2312} to 2.

$$Re(\frac{4623}{2312}+i)$$

The real part of \frac{4623}{2312}+i is \frac{4623}{2312}.

$$\frac{4623}{2312}$$