Solve V=(frac{sqrt{2}+isqrt{2}}{sqrt{2}-isqrt{2}})^2014

$$V = ( \frac { \sqrt { 2 } + i \sqrt { 2 } } { \sqrt { 2 } - i \sqrt { 2 } } ) ^ { 2014 }$$

Solve for V

$$V=-1$$

Steps for Solving Linear Equation

Combine \sqrt{2} and i\sqrt{2} to get \left(1+i\right)\sqrt{2}.

$$V=\left(\frac{\left(1+i\right)\sqrt{2}}{\sqrt{2}-i\sqrt{2}}\right)^{2014}$$

Combine \sqrt{2} and -i\sqrt{2} to get \left(1-i\right)\sqrt{2}.

$$V=\left(\frac{\left(1+i\right)\sqrt{2}}{\left(1-i\right)\sqrt{2}}\right)^{2014}$$

Cancel out \sqrt{2} in both numerator and denominator.

$$V=\left(\frac{1+i}{1-i}\right)^{2014}$$

Multiply both numerator and denominator of \frac{1+i}{1-i} by the complex conjugate of the denominator, 1+i.

$$V=\left(\frac{\left(1+i\right)\left(1+i\right)}{\left(1-i\right)\left(1+i\right)}\right)^{2014}$$

Do the multiplications in \frac{\left(1+i\right)\left(1+i\right)}{\left(1-i\right)\left(1+i\right)}.

$$V=\left(\frac{2i}{2}\right)^{2014}$$

Divide 2i by 2 to get i.

$$V=i^{2014}$$

Calculate i to the power of 2014 and get -1.

$$V=-1$$

Assign V

$$V≔-1$$