1. The problem is to expand the expression for $i$ (assuming $i$ is the imaginary unit where $i^2 = -1$) or to expand a given expression involving $i$. Since the user did not specify the exact expression, I will demonstrate the expansion of $(a+bi)^2$ where $a$ and $b$ are real numbers and $i$ is the imaginary unit. 2. Start with the expression: $$ (a + bi)^2 $$ 3. Use the formula for squaring a binomial: $$ (a + bi)^2 = a^2 + 2abi + (bi)^2 $$ 4. Simplify each term: - $a^2$ remains as is. - $2abi$ remains as is. - $(bi)^2 = b^2 i^2 = b^2 (-1) = -b^2$ because $i^2 = -1$. 5. Combine the terms: $$ a^2 + 2abi - b^2 $$ 6. Write the result as a complex number with real and imaginary parts: $$ (a^2 - b^2) + 2ab i $$ This is the expanded form of $(a + bi)^2$. If you meant a different expression involving $i$, please specify it for a precise expansion.