Solve Prove that i ^ 107 + i ^ 112 + i ^ 122 + i ^ 153 = 0 Add the following complex numbers | 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

$$i ^ { 107 } + i ^ { 112 } + i ^ { 122 } + i ^ { 153 } = 0$$

Verify

$\text{true}$

Solution Steps

Calculate $i$ to the power of $107$ and get $-i$.

$$-i+i^{112}+i^{122}+i^{153}=0$$

Calculate $i$ to the power of $112$ and get $1$.

$$-i+1+i^{122}+i^{153}=0$$

Calculate $i$ to the power of $122$ and get $-1$.

$$-i+1-1+i^{153}=0$$

Do the additions in $-i+1-1$.

$$i^{153}-i=0$$

Calculate $i$ to the power of $153$ and get $i$.

$$i-i=0$$

Subtract $i$ from $i$ to get $0$.

$$0=0$$

Compare $0$ and $0$.

$$\text{true}$$