Find the argument of the complex number $-1 + i$.
A$225^\circ$
B$-45^\circ$
C$45^\circ$
D$135^\circ$CORRECT
JUPEBMathematicsComplex Numbers
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Why the answer is D, and why the others tempt you.
The point $(-1, 1)$ lies in the second quadrant. The acute reference angle is $\tan^{-1}(1) = 45^\circ$, so the argument is $180^\circ - 45^\circ = 135^\circ$. Simply taking $\tan^{-1}\left(\dfrac{1}{-1}\right) = -45^\circ$ ignores the quadrant.
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