Find the exact value of open vertical bar, minus, 7, plus, i, close vertical bar∣−7+i∣.
Question
Find the exact value of open vertical bar, minus, 7, plus, i, close vertical bar∣−7+i∣.
Solution
The absolute value (or modulus) of a complex number a + bi is given by the formula √(a² + b²).
In this case, the complex number is -7 + i.
So, a = -7 and b = 1.
Substitute a and b into the formula:
= √((-7)² + 1²) = √(49 + 1) = √50 = 5√2
So, the exact value of ∣−7+i∣ is 5√2.
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