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Question

Answer

$\frac{1}{2} + s q r t \frac{1 + i}{2} = \frac{i q rs t + q rs t + 1}{2}$

Explanation

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$\frac{1}{2} + s q r t \frac{1 + i}{2} \overset{◯}{1} \frac{1}{2} + \frac{i q rs t + q rs t}{2} \overset{◯}{2} \frac{i q rs t + q rs t + 1}{2}$
①	Multiply $q rs t$ by $\frac{1 + i}{2}$ to get $\frac{i q rs t + q rs t}{2}$ . Step 1: Write $q rs t$ as a fraction by putting $1$ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $q rs t \cdot \frac{1 + i}{2} Step 1 \frac{q rs t}{1} \cdot \frac{1 + i}{2} Step 2 \frac{q rs t \cdot ( 1 + i )}{1 \cdot 2} = Step 3 \frac{q rs t + i q rs t}{2} = \frac{i q rs t + q rs t}{2}$
②	Add $\frac{1}{2}$ and $\frac{i q rs t + q rs t}{2}$ to get $\frac{i q rs t + q rs t + 1}{2}$ . To add expressions with the same denominators, we add the numerators and write the result over the common denominator. $\frac{1}{2} + \frac{i q rs t + q rs t}{2} = \frac{1}{2} + \frac{i q rs t + q rs t}{2} = \frac{1 + ( i q rs t + q rs t )}{2} = = \frac{i q rs t + q rs t + 1}{2}$

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