Write the amplitude and modulus of $- 4 - 4 i$ .

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Solution

Modulus of $- 4 - 4 i$ is $\sqrt{4^{2} + 4^{2}} = \sqrt{32} = 4 \sqrt{2}$ .
The point represented by the complex number lies in the third quadrant.
Now amplitude of the given complex number, is $- π + {tan}^{- 1} ∣ ∣ ∣ \frac{- 4}{- 4} ∣ ∣ ∣ = - \frac{3 π}{4}$ .

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