Solve (1 + i) ^ 4 * (1 + 1/i) ^ 4 = | Equatix - Math Solver

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Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

a⋅(b-2)=3b

Question

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

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 $16$.

$$16$$