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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∣.

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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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