Solve 1005*138^2/1000*180^2+j14*138^2/100*180

$$\frac{ 1005 \times { 138 }^{ 2 } }{ 1000 \times { 180 }^{ 2 } } +j \frac{ 14 \times { 138 }^{ 2 } }{ 100 \cdot 180 }$$

Evaluate

$$\frac{3703j}{250}+\frac{35443}{60000}$$

Solution Steps

Cancel out 5 in both numerator and denominator.

$$\frac{201\times 138^{2}}{200\times 180^{2}}+j\times \frac{14\times 138^{2}}{100\times 180}$$

Calculate 138 to the power of 2 and get 19044.

$$\frac{201\times 19044}{200\times 180^{2}}+j\times \frac{14\times 138^{2}}{100\times 180}$$

Multiply 201 and 19044 to get 3827844.

$$\frac{3827844}{200\times 180^{2}}+j\times \frac{14\times 138^{2}}{100\times 180}$$

Calculate 180 to the power of 2 and get 32400.

$$\frac{3827844}{200\times 32400}+j\times \frac{14\times 138^{2}}{100\times 180}$$

Multiply 200 and 32400 to get 6480000.

$$\frac{3827844}{6480000}+j\times \frac{14\times 138^{2}}{100\times 180}$$

Reduce the fraction \frac{3827844}{6480000} to lowest terms by extracting and canceling out 108.

$$\frac{35443}{60000}+j\times \frac{14\times 138^{2}}{100\times 180}$$

Cancel out 2 in both numerator and denominator.

$$\frac{35443}{60000}+j\times \frac{7\times 138^{2}}{50\times 180}$$

Calculate 138 to the power of 2 and get 19044.

$$\frac{35443}{60000}+j\times \frac{7\times 19044}{50\times 180}$$

Multiply 7 and 19044 to get 133308.

$$\frac{35443}{60000}+j\times \frac{133308}{50\times 180}$$

Multiply 50 and 180 to get 9000.

$$\frac{35443}{60000}+j\times \frac{133308}{9000}$$

Reduce the fraction \frac{133308}{9000} to lowest terms by extracting and canceling out 36.

$$\frac{35443}{60000}+j\times \frac{3703}{250}$$

Factor

$$\frac{529\left(1680j+67\right)}{60000}$$

Solution Steps

Cancel out 5 in both numerator and denominator.

$$factor(\frac{201\times 138^{2}}{200\times 180^{2}}+j\times \frac{14\times 138^{2}}{100\times 180})$$

Calculate 138 to the power of 2 and get 19044.

$$factor(\frac{201\times 19044}{200\times 180^{2}}+j\times \frac{14\times 138^{2}}{100\times 180})$$

Multiply 201 and 19044 to get 3827844.

$$factor(\frac{3827844}{200\times 180^{2}}+j\times \frac{14\times 138^{2}}{100\times 180})$$

Calculate 180 to the power of 2 and get 32400.

$$factor(\frac{3827844}{200\times 32400}+j\times \frac{14\times 138^{2}}{100\times 180})$$

Multiply 200 and 32400 to get 6480000.

$$factor(\frac{3827844}{6480000}+j\times \frac{14\times 138^{2}}{100\times 180})$$

Reduce the fraction \frac{3827844}{6480000} to lowest terms by extracting and canceling out 108.

$$factor(\frac{35443}{60000}+j\times \frac{14\times 138^{2}}{100\times 180})$$

Cancel out 2 in both numerator and denominator.

$$factor(\frac{35443}{60000}+j\times \frac{7\times 138^{2}}{50\times 180})$$

Calculate 138 to the power of 2 and get 19044.

$$factor(\frac{35443}{60000}+j\times \frac{7\times 19044}{50\times 180})$$

Multiply 7 and 19044 to get 133308.

$$factor(\frac{35443}{60000}+j\times \frac{133308}{50\times 180})$$

Multiply 50 and 180 to get 9000.

$$factor(\frac{35443}{60000}+j\times \frac{133308}{9000})$$

Reduce the fraction \frac{133308}{9000} to lowest terms by extracting and canceling out 36.

$$factor(\frac{35443}{60000}+j\times \frac{3703}{250})$$

Factor out \frac{529}{60000}.

$$\frac{529\left(67+1680j\right)}{60000}$$