Solve (1+i)^4(1+1/i)^4

$$( 1 + i ) ^ { 4 } ( 1 + \frac { 1 } { i } ) ^ { 4 }$$

Evaluate

$$16$$

Solution Steps

Calculate 1+i to the power of 4 and get -4.

$$-4\left(1+\frac{1}{i}\right)^{4}$$

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

$$-4\left(1+\frac{i}{-1}\right)^{4}$$

Divide i by -1 to get -i.

$$-4\left(1-i\right)^{4}$$

Calculate 1-i to the power of 4 and get -4.

$$-4\left(-4\right)$$

Multiply -4 and -4 to get 16.

$$16$$

Real Part

$$16$$

Solution Steps

Calculate 1+i to the power of 4 and get -4.

$$Re(-4\left(1+\frac{1}{i}\right)^{4})$$

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

$$Re(-4\left(1+\frac{i}{-1}\right)^{4})$$

Divide i by -1 to get -i.

$$Re(-4\left(1-i\right)^{4})$$

Calculate 1-i to the power of 4 and get -4.

$$Re(-4\left(-4\right))$$

Multiply -4 and -4 to get 16.

$$Re(16)$$

The real part of 16 is 16.

$$16$$