Subjects algebra

Complex Magnitude C47C3F

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1. The problem is to find the value of $|(2+2i)+/2|$. 2. First, clarify the expression. It seems to be $\left|\frac{2+2i}{2}\right|$, which means the magnitude of the complex number $\frac{2+2i}{2}$. 3. The magnitude (or modulus) of a complex number $a+bi$ is given by the formula $$|a+bi|=\sqrt{a^2+b^2}.$$ 4. Simplify the complex number inside the absolute value: $$\frac{2+2i}{2}=\frac{2}{2}+\frac{2i}{2}=1+i.$$ 5. Now find the magnitude of $1+i$: $$|1+i|=\sqrt{1^2+1^2}=\sqrt{1+1}=\sqrt{2}.$$ 6. Therefore, the value of $\left|\frac{2+2i}{2}\right|$ is $\sqrt{2}$.