Solve (1+i)^53/(1-i)^51

$$\frac { ( 1 + i ) ^ { 53 } } { ( 1 - i ) ^ { 51 } }$$

Evaluate

$$2$$

Solution Steps

Calculate 1+i to the power of 53 and get -67108864-67108864i.

$$\frac{-67108864-67108864i}{\left(1-i\right)^{51}}$$

Calculate 1-i to the power of 51 and get -33554432-33554432i.

$$\frac{-67108864-67108864i}{-33554432-33554432i}$$

Multiply both numerator and denominator by the complex conjugate of the denominator, -33554432+33554432i.

$$\frac{\left(-67108864-67108864i\right)\left(-33554432+33554432i\right)}{\left(-33554432-33554432i\right)\left(-33554432+33554432i\right)}$$

Do the multiplications in \frac{\left(-67108864-67108864i\right)\left(-33554432+33554432i\right)}{\left(-33554432-33554432i\right)\left(-33554432+33554432i\right)}.

$$\frac{4503599627370496}{2251799813685248}$$

Divide 4503599627370496 by 2251799813685248 to get 2.

$$2$$

Real Part

$$2$$

Solution Steps

Calculate 1+i to the power of 53 and get -67108864-67108864i.

$$Re(\frac{-67108864-67108864i}{\left(1-i\right)^{51}})$$

Calculate 1-i to the power of 51 and get -33554432-33554432i.

$$Re(\frac{-67108864-67108864i}{-33554432-33554432i})$$

Multiply both numerator and denominator of \frac{-67108864-67108864i}{-33554432-33554432i} by the complex conjugate of the denominator, -33554432+33554432i.

$$Re(\frac{\left(-67108864-67108864i\right)\left(-33554432+33554432i\right)}{\left(-33554432-33554432i\right)\left(-33554432+33554432i\right)})$$

Do the multiplications in \frac{\left(-67108864-67108864i\right)\left(-33554432+33554432i\right)}{\left(-33554432-33554432i\right)\left(-33554432+33554432i\right)}.

$$Re(\frac{4503599627370496}{2251799813685248})$$

Divide 4503599627370496 by 2251799813685248 to get 2.

$$Re(2)$$

The real part of 2 is 2.

$$2$$