The principal argument of z = 1 + 2i is which of the following?

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Multiple Choice

The principal argument of z = 1 + 2i is which of the following?

The principal argument is the angle that the complex number’s position makes with the positive real axis, taken in the standard range (−π, π]. For 1 + 2i, the point (1, 2) sits in the first quadrant, so the angle is arctan(2/1) = arctan 2. This evaluates to about 63.435 degrees, or 1.1071 radians. That is why this angle is the principal argument. The other angles would place the point in a different quadrant or on an axis (for example, −63.435° would correspond to a point with imaginary part negative, 0° is along the real axis, and 180° is the negative real axis), so they don’t match z = 1 + 2i.

The principal argument is the angle that the complex number’s position makes with the positive real axis, taken in the standard range (−π, π]. For 1 + 2i, the point (1, 2) sits in the first quadrant, so the angle is arctan(2/1) = arctan 2. This evaluates to about 63.435 degrees, or 1.1071 radians. That is why this angle is the principal argument.

The other angles would place the point in a different quadrant or on an axis (for example, −63.435° would correspond to a point with imaginary part negative, 0° is along the real axis, and 180° is the negative real axis), so they don’t match z = 1 + 2i.

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