Find the exact value of open vertical bar, 3, minus, 9, i, close vertical bar∣3−9i∣.
Question
Find the exact value of open vertical bar, 3, minus, 9, i, close vertical bar∣3−9i∣.
Solution
The given expression is the absolute value (or modulus) of a complex number. The absolute value of a complex number a + bi is given by √(a² + b²).
Here, a = 3 and b = -9.
Step 1: Square a and b. a² = 3² = 9 b² = (-9)² = 81
Step 2: Add a² and b². a² + b² = 9 + 81 = 90
Step 3: Take the square root of the result. √90 = 3√10
So, ∣3−9i∣ = 3√10.
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