How do you find the absolute value of 7+7i7+7i?

1 Answer
Feb 13, 2018

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\qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \ \ | 7 + 7i | \ = \ 7 \sqrt{ 2 }.

Explanation:

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"Recall that the definition of the absolute value of a "
"complex number," \ a + bi \ \ "is:"

\qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad | a + bi | \ = \ \sqrt{ a^2 + b^2 }.

"So, we have now:"

\qquad \qquad \qquad | 7 + 7i | \ = \ \sqrt{ 7^2 + 7^2 } \ = \ \sqrt{ 2 \cdot 7^2 } \ = \ 7 \sqrt{ 2 }.

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"Thus:"

\qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \ \ | 7 + 7i | \ = \ 7 \sqrt{ 2 }.