Solve |(1+i)^100/(1-i)^100|=

$$| \frac { ( 1 + i ) ^ { 100 } } { ( 1 - i ) ^ { 100 } } | =$$

Evaluate

$$1$$

Solution Steps

Calculate 1+i to the power of 100 and get -1125899906842624.

$$|\frac{-1125899906842624}{\left(1-i\right)^{100}}|$$

Calculate 1-i to the power of 100 and get -1125899906842624.

$$|\frac{-1125899906842624}{-1125899906842624}|$$

Divide -1125899906842624 by -1125899906842624 to get 1.

$$|1|$$

The modulus of a complex number a+bi is \sqrt{a^{2}+b^{2}}. The modulus of 1 is 1.

$$1$$

Real Part

$$1$$

Solution Steps

Calculate 1+i to the power of 100 and get -1125899906842624.

$$Re(|\frac{-1125899906842624}{\left(1-i\right)^{100}}|)$$

Calculate 1-i to the power of 100 and get -1125899906842624.

$$Re(|\frac{-1125899906842624}{-1125899906842624}|)$$

Divide -1125899906842624 by -1125899906842624 to get 1.

$$Re(|1|)$$

The modulus of a complex number a+bi is \sqrt{a^{2}+b^{2}}. The modulus of 1 is 1.

$$Re(1)$$

The real part of 1 is 1.

$$1$$