# Chapter 5.5.1 equation (5.16) | FX Book Questions | Forum

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Chapter 5.5.1 equation (5.16)
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January 28, 2015 - 1:27 pm
Member Since: December 16, 2014
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Hi All,

5.16 taken from the book:
H(w) = 0.5 + 0.5e^-jwt
= 0.5 + 0.5(cos(w)-jsin(w))
= 0.5 + 0.5(cos(0)-jsin(0))
= 0.5 + 0.5(1 - j0)
= 1.0 + j0

Can someone help me understand why this results in 1.0+j0 and not 1.0-j0?

Thanks,
-Jack

January 28, 2015 - 7:58 pm
Member Since: January 29, 2017
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You are correct - its a typo. But, since the imaginary part is 0 it doesn't affect anything.

Also note that there is a typo in the table above it Table 5.1 -- for the 3pi/4 row, the cos(w) value should be -0.707 while sin(w) = +0.707

- Will

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January 28, 2015 - 8:20 pm
Member Since: December 16, 2014
Forum Posts: 6
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Thank you! It's been over 10 years since my last math class and I thought it was my rusty skills.

I did catch the cos() and sin() as it was listed on the Errata page.

Speaking of the Errata page, it would be really helpful to us Kindle readers if you could include the section number in addition to the page number. The Kindle version of the book does not have page numbers.

Thanks again.
-Jack

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August 8, 2017 - 1:57 pm
Member Since: July 25, 2017
Forum Posts: 2
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Hi Will

If that is true, then the same applies here:Â

equation (5.18) should be 0 - j0

equation (5.45) should be 0 .526 - j0

equation (5.47) should be 10 - j0Â

Or am I wrong?

August 21, 2017 - 9:52 am
Member Since: January 29, 2017
Forum Posts: 693
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Yes, technically you are correct - but when the component value is 0 then -j0 and +j0 are semantically the same meaning "no imaginary component." I will update this in the next edition of the book for completeness.

- Will

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