Solve 1 + i ^ 10 + i ^ 100 - i ^ 1000 = | 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

$$1+i^{10}+i^{100}-i^{1000}=$$

Evaluate

$0$

Solution Steps

Calculate $i$ to the power of $10$ and get $-1$.

$$1-1+i^{100}-i^{1000}$$

Subtract $1$ from $1$ to get $0$.

$$i^{100}-i^{1000}$$

Calculate $i$ to the power of $100$ and get $1$.

$$1-i^{1000}$$

Calculate $i$ to the power of $1000$ and get $1$.

$$1-1$$

Subtract $1$ from $1$ to get $0$.

$$0$$

Real Part

$0$

Solution Steps

Calculate $i$ to the power of $10$ and get $-1$.

$$Re(1-1+i^{100}-i^{1000})$$

Subtract $1$ from $1$ to get $0$.

$$Re(i^{100}-i^{1000})$$

Calculate $i$ to the power of $100$ and get $1$.

$$Re(1-i^{1000})$$

Calculate $i$ to the power of $1000$ and get $1$.

$$Re(1-1)$$

Subtract $1$ from $1$ to get $0$.

$$Re(0)$$

The real part of $0$ is $0$.

$$0$$