Find the absolute value. |-9i|

Absolute Value Calculation: What is the absolute value of a + bi? |a + bi| = sqrt(a^2 + b^2)Expression Substitution: Which expression represents |-9i|? |a + bi| = sqrt(a^2 + b^2) Substitute a = 0 and b = -9. |-9i| = sqrt(0² + (-9)²)Expression Simplification: Simplify 0^2 + (-9)^2. 0^2 + (-9)^2 = 0 * 0 + (-9) * (-9) =0 + 81 = 81Final Value Calculation: Simplify sqrt(81) to find the value of |-9i|. |-9i| = sqrt(81) = sqrt(9^2) =9

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Find the absolute value. $\newline$ $|-9i|$

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Math Problems

Algebra 2

Absolute values of complex numbers

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Q. Find the absolute value.

\newline

|-9i|

Absolute Value Calculation: What is the absolute value of $a + bi$ ? $\newline$ $|a + bi| = \sqrt{a^2 + b^2}$
Expression Substitution: For $|-9i|$ , $a = 0$ and $b = -9$ $\newline$ Use $|a + bi| = \sqrt{a^2 + b^2}$ and substitute the values. $\newline$ $|-9i| = \sqrt{0^2 + (-9)^2}$
Expression Simplification: Simplify $0^2 + (-9)^2$ . $\newline$ $0^2 + (-9)^2$ $= 0 \times 0 + (-9\times (-9)$ $\newline$ $= 0 + 81$ $= 81$
Final Value Calculation: Simplify $\sqrt{81}$ to find the value of $|-9i|$ . $|-9i| = \sqrt{81} = \sqrt{9^2} = 9$