Solve 2(4-2)^2/3(7-4i)

$$\frac { 2 ( 4 - 2 ) ^ { 2 } } { 3 ( 7 - 4 i ) }$$

Evaluate

$$\frac{56}{195}+\frac{32}{195}i\approx 0.287179487+0.164102564i$$

Solution Steps

Subtract 2 from 4 to get 2.

$$\frac{2\times 2^{2}}{3\left(7-4i\right)}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{2\times 4}{3\left(7-4i\right)}$$

Multiply 2 and 4 to get 8.

$$\frac{8}{3\left(7-4i\right)}$$

Multiply 3 and 7-4i to get 21-12i.

$$\frac{8}{21-12i}$$

Multiply both numerator and denominator by the complex conjugate of the denominator, 21+12i.

$$\frac{8\left(21+12i\right)}{\left(21-12i\right)\left(21+12i\right)}$$

Do the multiplications in \frac{8\left(21+12i\right)}{\left(21-12i\right)\left(21+12i\right)}.

$$\frac{168+96i}{585}$$

Divide 168+96i by 585 to get \frac{56}{195}+\frac{32}{195}i.

$$\frac{56}{195}+\frac{32}{195}i$$

Real Part

$$\frac{56}{195} = 0.28717948717948716$$

Solution Steps

Subtract 2 from 4 to get 2.

$$Re(\frac{2\times 2^{2}}{3\left(7-4i\right)})$$

Calculate 2 to the power of 2 and get 4.

$$Re(\frac{2\times 4}{3\left(7-4i\right)})$$

Multiply 2 and 4 to get 8.

$$Re(\frac{8}{3\left(7-4i\right)})$$

Multiply 3 and 7-4i to get 21-12i.

$$Re(\frac{8}{21-12i})$$

Multiply both numerator and denominator of \frac{8}{21-12i} by the complex conjugate of the denominator, 21+12i.

$$Re(\frac{8\left(21+12i\right)}{\left(21-12i\right)\left(21+12i\right)})$$

Do the multiplications in \frac{8\left(21+12i\right)}{\left(21-12i\right)\left(21+12i\right)}.

$$Re(\frac{168+96i}{585})$$

Divide 168+96i by 585 to get \frac{56}{195}+\frac{32}{195}i.

$$Re(\frac{56}{195}+\frac{32}{195}i)$$

The real part of \frac{56}{195}+\frac{32}{195}i is \frac{56}{195}.

$$\frac{56}{195}$$