Solve i^3+1/i322553

$${ i }^{ 3 } + \frac{ 1 }{ i3 } 22553$$

Evaluate

$$-\frac{22556}{3}i\approx -7518.666666667i$$

Solution Steps

Calculate i to the power of 3 and get -i.

$$-i+\frac{1}{3i}\times 22553$$

Multiply both numerator and denominator of \frac{1}{3i} by imaginary unit i.

$$-i+\frac{i}{-3}\times 22553$$

Divide i by -3 to get -\frac{1}{3}i.

$$-i-\frac{1}{3}i\times 22553$$

Multiply -\frac{1}{3}i and 22553 to get -\frac{22553}{3}i.

$$-i-\frac{22553}{3}i$$

Subtract \frac{22553}{3}i from -i to get -\frac{22556}{3}i.

$$-\frac{22556}{3}i$$

Real Part

$$0$$

Solution Steps

Calculate i to the power of 3 and get -i.

$$Re(-i+\frac{1}{3i}\times 22553)$$

Multiply both numerator and denominator of \frac{1}{3i} by imaginary unit i.

$$Re(-i+\frac{i}{-3}\times 22553)$$

Divide i by -3 to get -\frac{1}{3}i.

$$Re(-i-\frac{1}{3}i\times 22553)$$

Multiply -\frac{1}{3}i and 22553 to get -\frac{22553}{3}i.

$$Re(-i-\frac{22553}{3}i)$$

Subtract \frac{22553}{3}i from -i to get -\frac{22556}{3}i.

$$Re(-\frac{22556}{3}i)$$

The real part of -\frac{22556}{3}i is 0.

$$0$$