Solve 1005*13.8^2/1000*180^2+j14*13.8^2/100*180

$$\frac{ 1005 \times { 13.8 }^{ 2 } }{ 1000 \times { 180 }^{ 2 } } +j \frac{ 14 \times { 13.8 }^{ 2 } }{ 100 \cdot 180 }$$

Evaluate

$$\frac{3703j}{25000}+\frac{35443}{6000000}$$

Solution Steps

Cancel out 5 in both numerator and denominator.

$$\frac{201\times 13.8^{2}}{200\times 180^{2}}+j\times \frac{14\times 13.8^{2}}{100\times 180}$$

Calculate 13.8 to the power of 2 and get 190.44.

$$\frac{201\times 190.44}{200\times 180^{2}}+j\times \frac{14\times 13.8^{2}}{100\times 180}$$

Multiply 201 and 190.44 to get 38278.44.

$$\frac{38278.44}{200\times 180^{2}}+j\times \frac{14\times 13.8^{2}}{100\times 180}$$

Calculate 180 to the power of 2 and get 32400.

$$\frac{38278.44}{200\times 32400}+j\times \frac{14\times 13.8^{2}}{100\times 180}$$

Multiply 200 and 32400 to get 6480000.

$$\frac{38278.44}{6480000}+j\times \frac{14\times 13.8^{2}}{100\times 180}$$

Expand \frac{38278.44}{6480000} by multiplying both numerator and the denominator by 100.

$$\frac{3827844}{648000000}+j\times \frac{14\times 13.8^{2}}{100\times 180}$$

Reduce the fraction \frac{3827844}{648000000} to lowest terms by extracting and canceling out 108.

$$\frac{35443}{6000000}+j\times \frac{14\times 13.8^{2}}{100\times 180}$$

Cancel out 2 in both numerator and denominator.

$$\frac{35443}{6000000}+j\times \frac{7\times 13.8^{2}}{50\times 180}$$

Calculate 13.8 to the power of 2 and get 190.44.

$$\frac{35443}{6000000}+j\times \frac{7\times 190.44}{50\times 180}$$

Multiply 7 and 190.44 to get 1333.08.

$$\frac{35443}{6000000}+j\times \frac{1333.08}{50\times 180}$$

Multiply 50 and 180 to get 9000.

$$\frac{35443}{6000000}+j\times \frac{1333.08}{9000}$$

Expand \frac{1333.08}{9000} by multiplying both numerator and the denominator by 100.

$$\frac{35443}{6000000}+j\times \frac{133308}{900000}$$

Reduce the fraction \frac{133308}{900000} to lowest terms by extracting and canceling out 36.

$$\frac{35443}{6000000}+j\times \frac{3703}{25000}$$

Factor

$$\frac{529\left(1680j+67\right)}{6000000}$$

Solution Steps

Cancel out 5 in both numerator and denominator.

$$factor(\frac{201\times 13.8^{2}}{200\times 180^{2}}+j\times \frac{14\times 13.8^{2}}{100\times 180})$$

Calculate 13.8 to the power of 2 and get 190.44.

$$factor(\frac{201\times 190.44}{200\times 180^{2}}+j\times \frac{14\times 13.8^{2}}{100\times 180})$$

Multiply 201 and 190.44 to get 38278.44.

$$factor(\frac{38278.44}{200\times 180^{2}}+j\times \frac{14\times 13.8^{2}}{100\times 180})$$

Calculate 180 to the power of 2 and get 32400.

$$factor(\frac{38278.44}{200\times 32400}+j\times \frac{14\times 13.8^{2}}{100\times 180})$$

Multiply 200 and 32400 to get 6480000.

$$factor(\frac{38278.44}{6480000}+j\times \frac{14\times 13.8^{2}}{100\times 180})$$

Expand \frac{38278.44}{6480000} by multiplying both numerator and the denominator by 100.

$$factor(\frac{3827844}{648000000}+j\times \frac{14\times 13.8^{2}}{100\times 180})$$

Reduce the fraction \frac{3827844}{648000000} to lowest terms by extracting and canceling out 108.

$$factor(\frac{35443}{6000000}+j\times \frac{14\times 13.8^{2}}{100\times 180})$$

Cancel out 2 in both numerator and denominator.

$$factor(\frac{35443}{6000000}+j\times \frac{7\times 13.8^{2}}{50\times 180})$$

Calculate 13.8 to the power of 2 and get 190.44.

$$factor(\frac{35443}{6000000}+j\times \frac{7\times 190.44}{50\times 180})$$

Multiply 7 and 190.44 to get 1333.08.

$$factor(\frac{35443}{6000000}+j\times \frac{1333.08}{50\times 180})$$

Multiply 50 and 180 to get 9000.

$$factor(\frac{35443}{6000000}+j\times \frac{1333.08}{9000})$$

Expand \frac{1333.08}{9000} by multiplying both numerator and the denominator by 100.

$$factor(\frac{35443}{6000000}+j\times \frac{133308}{900000})$$

Reduce the fraction \frac{133308}{900000} to lowest terms by extracting and canceling out 36.

$$factor(\frac{35443}{6000000}+j\times \frac{3703}{25000})$$

Factor out \frac{529}{6000000}.

$$\frac{529\left(67+1680j\right)}{6000000}$$