Solve 7i/9i/frac{-7i{+9i}}

$$\frac { \frac { 7 i } { 9 i } } { \frac { - 7 i } { + 9 i } }$$

Evaluate

$$-1$$

Solution Steps

Divide \frac{7i}{9i} by \frac{-7i}{9i} by multiplying \frac{7i}{9i} by the reciprocal of \frac{-7i}{9i}.

$$\frac{7i\times \left(9i\right)}{9i\times \left(-7i\right)}$$

To divide powers of the same base, subtract the numerator's exponent from the denominator's exponent.

$$\frac{7i}{-7i\times \left(9i\right)^{0}}$$

Calculate 9i to the power of 0 and get 1.

$$\frac{7i}{-7i}$$

Divide 7i by -7i to get -1.

$$-1$$

Real Part

$$-1$$

Solution Steps

Divide \frac{7i}{9i} by \frac{-7i}{9i} by multiplying \frac{7i}{9i} by the reciprocal of \frac{-7i}{9i}.

$$Re(\frac{7i\times \left(9i\right)}{9i\times \left(-7i\right)})$$

To divide powers of the same base, subtract the numerator's exponent from the denominator's exponent.

$$Re(\frac{7i}{-7i\times \left(9i\right)^{0}})$$

Calculate 9i to the power of 0 and get 1.

$$Re(\frac{7i}{-7i})$$

Divide 7i by -7i to get -1.

$$Re(-1)$$

The real part of -1 is -1.

$$-1$$