Entering complex numbers in exponential form

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August 11th, 2009, 05:49 PM

Hamilc

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Entering complex numbers in exponential form

TI 84 Plu SE

I am trying to enter a complex number in exponential form and having trouble.

My calculator is in DEGREE mode. I enter e^(i45) and expect to get .707 + i.707 Instead I get .525 + .850i. The calculator does not seem to recognize 45 as degrees and instead treats it as radians. I have read two references that say I should be able to enter the angle in degrees. What am I doing wrong???

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August 11th, 2009, 06:39 PM

archnaid

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Quote:

In degree mode, complex identities such as e^(iq) = cos(q) + i sin(q) are not generally
true because the values for cos and sin are converted to radians, while those for e^() are
not. For example, e^(i45) = cos(45) + i sin(45) is treated internally as
e^(i45) = cos(p/4) + i sin(p/4). Complex identities are always true in radian mode.

Ti-84+/SE Manual

Quote:

Caution: The angle must be in radians, even if the calculator is in degree mode, and the imaginary symbol i is required.

First Google result for 'ti-84 complex numbers'

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August 11th, 2009, 08:39 PM

Hamilc

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What you are saying is obviously true. I think the manual is VERY confusing. If I am in degree mode and enter e^(i45) and it is converted to cos(45) + isin(45) I assume they mean that even though the argument of e^(i45) is in degrees, the term cos(45) considers the 45 to be in radians. To make maters worse, if you are in degree mode and enter .7 + .7i then convert to polar using math>complex, you will get e^(45i) in degrees. then enter exactly what yousee on the display, i.e. 1e^(45i) and you don't get back what you started with. I also read the book TI 84 for dummies and it says you can enter the exponention version in degrees or radians. TI needs to do some improvement here.

Anyway, I know how to do a work around even though this seems to me like a big blunder.

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August 11th, 2009, 08:56 PM

archnaid

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Yeah, the manual wasn't very clear. What I understand it to be saying is that in degree mode, the calculator takes cos(45), converts it to cos(pi/2), then evaluates it; but no matter the mode, it does not do this for certain constructs, including exponentials:

Quote:

Radian mode is recommended for complex number calculations. Internally, the TI-84
Plus converts all entered trigonometric values to radians, but it does not convert values
for exponential, logarithmic, or hyperbolic functions.

Care sharing your work around? I've an 89 so it won't really help me, but I'm sure there are others who've run into this.

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