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Find the absolute value. $|-7i|$

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Absolute values of complex numbers

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Q. Find the absolute value.

|-7i|

Complex Number Absolute Value Formula: The absolute value of a complex number in the form $a + bi$ is given by the formula $|a + bi| = \sqrt{a^2 + b^2}$ , where $a$ is the real part and $b$ is the imaginary part.
Substitute Real and Imaginary Parts: In the expression |\(-7i| ext{, the real part } a \text{ is } $0$ \text{ and the imaginary part } b \text{ is } $-7$ . \text{ Therefore, we substitute } a = $0$ \text{ and } b = $-7$ \text{ into the formula.} $\newline$ $|-7i| = \sqrt{0^2 + (-7)^2}$
Calculate Squares: We calculate $0^2$ and $(-7)^2$ . Since $0^2 = 0$ and $(-7)^2 = 49$ , we have: $\newline$ $|-7i| = \sqrt{0 + 49}$
Simplify Square Root: Simplify the expression inside the square root: $|-7i| = \sqrt{49}$
Final Absolute Value Calculation: The square root of $49$ is $7$ , so the absolute value of $|-7i|$ is: $\newline$ $|-7i| = 7$

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