Solve [(3i-i)^2+2]:i

$$[ ( 3 i - i ) ^ { 2 } + 2 ] : i$$

Evaluate

$$2i$$

Solution Steps

Subtract i from 3i to get 2i.

$$\frac{\left(2i\right)^{2}+2}{i}$$

Calculate 2i to the power of 2 and get -4.

$$\frac{-4+2}{i}$$

Add -4 and 2 to get -2.

$$\frac{-2}{i}$$

Multiply both numerator and denominator by imaginary unit i.

$$\frac{-2i}{-1}$$

Divide -2i by -1 to get 2i.

$$2i$$

Real Part

$$0$$

Solution Steps

Subtract i from 3i to get 2i.

$$Re(\frac{\left(2i\right)^{2}+2}{i})$$

Calculate 2i to the power of 2 and get -4.

$$Re(\frac{-4+2}{i})$$

Add -4 and 2 to get -2.

$$Re(\frac{-2}{i})$$

Multiply both numerator and denominator of \frac{-2}{i} by imaginary unit i.

$$Re(\frac{-2i}{-1})$$

Divide -2i by -1 to get 2i.

$$Re(2i)$$

The real part of 2i is 0.

$$0$$