Difference between revisions of "Manuals/calci/IMSIN"

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<div style="font-size:30px">'''IMSIN(z)'''</div><br/>
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<div style="font-size:30px">'''IMSIN (ComplexNumber) '''</div><br/>
* where z is any real number
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*<math>ComplexNumber</math> is any complex number of the form x+iy.
 +
**IMSIN(),returns the sine of a complex number.
 +
 
 
==Description==
 
==Description==
 
+
*This function gives the sin value of any complex number.  
*This function gives the sin value of 'iz'.  
+
*Consider the complex number in the form of <math>x+iy</math>
*Where 'iz' is the complex number in the form of <math>x+iy</math>.i.e. x&y are the real numbers.
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*x & y are the real numbers.
*'i' imaginary unit <math>i=\sqrt(-1)</math>
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*'i' is the imaginary unit <math>i=\sqrt{-1}</math>
 
*Also x is  called the real part & y is the imaginary part of a complex number.
 
*Also x is  called the real part & y is the imaginary part of a complex number.
*'COMPLEX' is the function used to convert real & imaginary numbers in to a complex number.
+
*[[Manuals/calci/COMPLEX| COMPLEX]] is the function used to convert Real & Imaginary numbers in to a complex number.
 
*<math>sin(x+iy)</math> is defined by <math>sin(x+iy)=sin(x)cosh(y)-icos(x)sinh(y)</math>
 
*<math>sin(x+iy)</math> is defined by <math>sin(x+iy)=sin(x)cosh(y)-icos(x)sinh(y)</math>
  
 
== Examples ==
 
== Examples ==
'''IMSIN(iz)'''
+
'''IMSIN (ComplexNumber)'''
*'''iz''' is the complex number.  
+
*'''ComplexNumber''' is any complex number.  
  
 
{|id="TABLE1" class="SpreadSheet blue"
 
{|id="TABLE1" class="SpreadSheet blue"
  
 
|- class="even"
 
|- class="even"
|'''IMSIN(iz)'''
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|'''IMSIN(ComplexNumber)'''
|'''Value(Radian)'''
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|'''Value'''
  
 
|- class="odd"
 
|- class="odd"
 
| IMSIN("4+5i")
 
| IMSIN("4+5i")
| -56.162-i48.502
+
| -56.16227422023234-ⅈ48.5024552417709
  
 
|- class="even"
 
|- class="even"
 
| IMSIN("4-5i")
 
| IMSIN("4-5i")
| 56.162-i48.502
+
| -56.16227422023234+ⅈ48.5024552417709
  
 
|- class="odd"
 
|- class="odd"
 
| IMSIN("4")
 
| IMSIN("4")
| 0.756802
+
| -0.7568024953079282+ⅈ0
 
|}
 
|}
 +
 +
==Related Videos==
 +
 +
{{#ev:youtube|gkW9PxDvKKk|280|center|Trigonometric Form of Complex Numbers}}
  
 
==See Also==
 
==See Also==
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*[http://en.wikipedia.org/wiki/Trigonometric_functions List of Trigonometric Functions]
 
*[http://en.wikipedia.org/wiki/Trigonometric_functions List of Trigonometric Functions]
 
*[http://en.wikipedia.org/wiki/Hyperbolic_function  Hyperbolic Function]
 
*[http://en.wikipedia.org/wiki/Hyperbolic_function  Hyperbolic Function]
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 +
 +
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*[[Z_API_Functions | List of Main Z Functions]]
 +
 +
*[[ Z3 |  Z3 home ]]

Latest revision as of 15:49, 18 July 2018

IMSIN (ComplexNumber)


  • is any complex number of the form x+iy.
    • IMSIN(),returns the sine of a complex number.

Description

  • This function gives the sin value of any complex number.
  • Consider the complex number in the form of
  • x & y are the real numbers.
  • 'i' is the imaginary unit
  • Also x is called the real part & y is the imaginary part of a complex number.
  • COMPLEX is the function used to convert Real & Imaginary numbers in to a complex number.
  • is defined by

Examples

IMSIN (ComplexNumber)

  • ComplexNumber is any complex number.
IMSIN(ComplexNumber) Value
IMSIN("4+5i") -56.16227422023234-ⅈ48.5024552417709
IMSIN("4-5i") -56.16227422023234+ⅈ48.5024552417709
IMSIN("4") -0.7568024953079282+ⅈ0

Related Videos

Trigonometric Form of Complex Numbers

See Also


References