What is the angle of a complex number with a coefficient of i?

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The discussion revolves around determining the angle of two complex numbers, A and B, where A=2exp[-ikz] and B=2iexp[-ikz]. The angle of A is identified as -kz, while the angle for B is unclear due to the presence of the coefficient i. A hint is provided that relates i to the exponential form, specifically i = e^(iπ/2), which helps in understanding how to calculate the angle for B. The angle for B can be derived by adding π/2 to the angle of A, resulting in the angle of B being -kz + π/2. This discussion highlights the importance of recognizing the role of the imaginary unit in complex number angles.
roz77
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I have two complex numbers, let's call them A and B. A=2exp[-ikz], and B=2iexp[-ikz]. I have to figure out the angle of these two numbers, and I am just completely drawing a blank on B. I know that the angle of A is just -kz, but I can't remember how to figure it out for part B. I can't remember what that i in front does.
 
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hi roz77! :smile:

hint: i = ei(what?) :wink:
 
k and z are just random variables that were in the problem. I know that when its exp[ikz], the angle is kz, but I'm not sure when it's iexp[ikz].
 
no, i mean solve i = ei(something) :smile:
 
<br /> i=e^{\frac{\pi i}{2}}<br />
 
Question: A clock's minute hand has length 4 and its hour hand has length 3. What is the distance between the tips at the moment when it is increasing most rapidly?(Putnam Exam Question) Answer: Making assumption that both the hands moves at constant angular velocities, the answer is ## \sqrt{7} .## But don't you think this assumption is somewhat doubtful and wrong?

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