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

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Answer 1 · 2018-02-13T09:39:14

# \ #

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

# \ #

# "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 }. #

# \ #

# "Thus:" #

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