In Exercises 21–28, divide and express the result in standard form. 2i/(1 + i)

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Identify the problem: You need to divide the complex number \$2i$ by the complex number $(1 + i)$ and express the result in standard form $a + bi$, where $a$ and $b$ are real numbers.

To divide complex numbers, multiply the numerator and denominator by the conjugate of the denominator. The conjugate of $(1 + i)$ is $(1 - i)$. So, multiply numerator and denominator by $(1 - i)$:

\[\frac{2i}{1 + i} \times \frac{1 - i}{1 - i}\]

Use the distributive property (FOIL) to expand both numerator and denominator:

- Numerator: $2i \times (1 - i) = 2i - 2i^2$

- Denominator: $(1 + i)(1 - i) = 1 - i^2$

Recall that $i^2 = -1$, so simplify both numerator and denominator using this fact, then combine like terms to write the expression in the form $a + bi$.

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