Solve -3+7i/8^2-10i^2(8+10i)

$$\frac { - 3 + 7 i } { 8 ^ { 2 } - 10 i ^ { 2 } } ( 8 + 10 i )$$

Evaluate

$$-\frac{47}{37}+\frac{13}{37}i\approx -1.27027027+0.351351351i$$

Solution Steps

Calculate 8 to the power of 2 and get 64.

$$\frac{-3+7i}{64-10i^{2}}\left(8+10i\right)$$

Calculate i to the power of 2 and get -1.

$$\frac{-3+7i}{64-10\left(-1\right)}\left(8+10i\right)$$

Multiply 10 and -1 to get -10.

$$\frac{-3+7i}{64-\left(-10\right)}\left(8+10i\right)$$

The opposite of -10 is 10.

$$\frac{-3+7i}{64+10}\left(8+10i\right)$$

Add 64 and 10 to get 74.

$$\frac{-3+7i}{74}\left(8+10i\right)$$

Divide -3+7i by 74 to get -\frac{3}{74}+\frac{7}{74}i.

$$\left(-\frac{3}{74}+\frac{7}{74}i\right)\left(8+10i\right)$$

Multiply -\frac{3}{74}+\frac{7}{74}i and 8+10i to get -\frac{47}{37}+\frac{13}{37}i.

$$-\frac{47}{37}+\frac{13}{37}i$$

Real Part

$$-\frac{47}{37} = -1\frac{10}{37} = -1.2702702702702702$$

Solution Steps

Calculate 8 to the power of 2 and get 64.

$$Re(\frac{-3+7i}{64-10i^{2}}\left(8+10i\right))$$

Calculate i to the power of 2 and get -1.

$$Re(\frac{-3+7i}{64-10\left(-1\right)}\left(8+10i\right))$$

Multiply 10 and -1 to get -10.

$$Re(\frac{-3+7i}{64-\left(-10\right)}\left(8+10i\right))$$

The opposite of -10 is 10.

$$Re(\frac{-3+7i}{64+10}\left(8+10i\right))$$

Add 64 and 10 to get 74.

$$Re(\frac{-3+7i}{74}\left(8+10i\right))$$

Divide -3+7i by 74 to get -\frac{3}{74}+\frac{7}{74}i.

$$Re(\left(-\frac{3}{74}+\frac{7}{74}i\right)\left(8+10i\right))$$

Multiply -\frac{3}{74}+\frac{7}{74}i and 8+10i to get -\frac{47}{37}+\frac{13}{37}i.

$$Re(-\frac{47}{37}+\frac{13}{37}i)$$

The real part of -\frac{47}{37}+\frac{13}{37}i is -\frac{47}{37}.

$$-\frac{47}{37}$$