Question

Perform each operation. Write answers in standard form. -5i(3-i)²

Accepted Answer

First, recognize that the problem requires you to simplify the expression $$-5i(3 - i)^2$ and write the answer in standard form, which is a + bi$ where a$ and b$ are real numbers. Start by expanding the squared term (3$$ - $$i)^2. $$Use the formula for squaring a binomial: $$(a - b)^2$ = a^2$ - 2ab + b^2$. Here, a = 3$ and b = i$, so write out the expansion as 3^2$ - 2 	imes 3 	imes i + i^2$. Calculate each part of the expansion: 3^2$ = 9$$, $$-2 	imes 3 	imes i = -6i$$, and recall that $$i^2 = -1$. Substitute these values back into the expression to get 9 - 6i + (-1$$)$$. Combine the real terms 9$ and -1$ to simplify the expression inside the parentheses to 8 - 6i$. Now, multiply this result by -5i$, so you have -5i(8 - 6i$$)$$. Distribute -5i$ across both terms inside the parentheses: multiply -5i$$ 	imes 8$$ and -5i$$ 	imes (-6i)$$. Remember to use the property i^2$ = -1$$ when simplifying the product involving $$i^2. $$After this, combine like terms to write the expression in the form $$a + bi.$$

Perform each operation. Write answers in standard form. -5i(3-i)²

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Key Concepts

Complex Numbers and Imaginary Unit

Exponentiation of Binomials

Multiplication of Complex Numbers