4x Find the value of inn. 1 i^wedge 345= 2 i^wedge 478= 3. i^wedge 295= 4 i^wedge 192=1 5 in999= 6 i^wedge 622=

## Step 1: Simplify the exponents using the property $i^2 = -1$<br />### We simplify the exponents by dividing them by 2 and considering the remainder. Remember that $i^2 = -1$, $i^3 = -i$, and $i^4 = 1$. Any exponent can be reduced to one of these four cases.<br /><br />## Step 2: Calculate $i^{345}$<br />### $345 = 2 \cdot 172 + 1$, so $i^{345} = (i^2)^{172} \cdot i = (-1)^{172} \cdot i = 1 \cdot i = i$<br /><br />## Step 3: Calculate $i^{478}$<br />### $478 = 2 \cdot 239$, so $i^{478} = (i^2)^{239} = (-1)^{239} = -1$<br /><br />## Step 4: Calculate $i^{295}$<br />### $295 = 2 \cdot 147 + 1$, so $i^{295} = (i^2)^{147} \cdot i = (-1)^{147} \cdot i = -1 \cdot i = -i$<br /><br />## Step 5: Calculate $i^{192}$<br />### $192 = 2 \cdot 96$, so $i^{192} = (i^2)^{96} = (-1)^{96} = 1$<br /><br />## Step 6: Calculate $i^{999}$<br />### $999 = 2 \cdot 499 + 1$, so $i^{999} = (i^2)^{499} \cdot i = (-1)^{499} \cdot i = -1 \cdot i = -i$<br /><br />## Step 7: Calculate $i^{622}$<br />### $622 = 2 \cdot 311$, so $i^{622} = (i^2)^{311} = (-1)^{311} = -1$