Quick questions on Complex number arithmetic and the Argand plane in HSC Mathematics Extension 2: Cartesian and polar form, modulus, argument, conjugate and geometric interpretation

Q: What is wrong quadrant for the argument?

Using (y/x) blindly puts every argument in (-π/2, π/2). Check the signs of x and y to place the angle in the correct quadrant.

2short Q&A pairs drawn directly from our worked dot-point answer. For full context and worked exam questions, read the parent dot-point page.

What is wrong quadrant for the argument?

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Using

\arctan(y/x)

blindly puts every argument in

(-\pi/2, \pi/2)

. Check the signs of

x

and

y

to place the angle in the correct quadrant.

What is not realising the denominator?

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Division is only complete once the denominator is a real number. Multiply by the conjugate, do not stop at a complex denominator.

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