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2 Minutes for this? No chance (1 Viewer)
- Thread starter v.tex
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C2H6O
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- 2025
with this question i wouldve written out the formula for |z| which is 
you can notice easily that the maximum and minimum values of θ return |z|=1, which from the options available is the maximum. then if you notice that at θ=pi/4, the function is at a symmetrical point, because both cos and sin increase and decrease at opposite rates on either side of pi/4, if that makes sense. so you know θ=pi/4 is a minimum or maximum, but given that 1 must have been a maximum, then pi/4 is the minimum, which gives 1/sqrt2 when subbed in. (idk how foolproof this is, but i got B without looking at the solution or doing much working)
you can notice easily that the maximum and minimum values of θ return |z|=1, which from the options available is the maximum. then if you notice that at θ=pi/4, the function is at a symmetrical point, because both cos and sin increase and decrease at opposite rates on either side of pi/4, if that makes sense. so you know θ=pi/4 is a minimum or maximum, but given that 1 must have been a maximum, then pi/4 is the minimum, which gives 1/sqrt2 when subbed in. (idk how foolproof this is, but i got B without looking at the solution or doing much working)