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Modulus and principal argument in the third quadrant

Let z=−1−3iz=-1-\sqrt3i.

(i) State the value of ∣−1−3i∣|-1-\sqrt3i| and arg⁡(−1−3i)\arg(-1-\sqrt3i).

(ii) Give the geometrical meanings of the statements “∣−1−3i∣|-1-\sqrt3i|” and “arg⁡(−1−3i)\arg(-1-\sqrt3i)”.

CJC · Discussion · Question 10

Choose the quadrant before assigning the principal argument.

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