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Line 1: − + + + − Syntax+ + + + + + + + + − </div></div>+ − ---- − <div id="4SpaceContent" align="left"><div class="ZEditBox" align="justify"> − Remarks+ + + + − </div></div>+ − ---- − <div id="2SpaceContent" align="left"><div class="ZEditBox" align="justify"> − Examples+ + + + + − </div></div> − ---- − <div id="8SpaceContent" align="left"><div class="ZEditBox" align="justify">'''<font face="Times New Roman">''''''''''''<font size="6"> </font>''' '''''''''</font>'''</div></div> − ---- − <div id="11SpaceContent" align="left"><div class="ZEditBox mceEditable" align="justify"> − <font size="5">Description</font>+ − + − </div></div> − ---- − <div id="5SpaceContent" class="zcontent" align="left"><div class="ZEditBox" align="justify"> − − <font color="#484848"><font face="Arial, sans-serif"><font size="2">This function calculates a complex number in a + bi or a + bj text format raised to a power.</font></font></font> − − </div></div> − ---- − <div id="10SpaceContent" class="zcontent" align="left"><div class="ZEditBox" align="justify"><font size="6">'''<font face="Arial">IMPOWER</font>'''</font></div></div> − ---- − <div id="1SpaceContent" class="zcontent" align="left"><div class="ZEditBox" align="justify"> − − * <font color="#484848"><font face="Arial, sans-serif"><font size="2">num can be an integer, fractional, or negative. </font></font></font> − * <font color="#484848"><font face="Arial, sans-serif"><font size="2">A complex number raised to a power is calculated as follows: </font></font></font> − − <font color="#484848"></font> − − <font color="#484848"><font face="Arial, sans-serif"><font size="2"></font></font></font> − − <font color="#484848"></font> − − <font color="#484848"><font face="Arial, sans-serif"><font size="2"></font></font></font> − − <font color="#484848"></font> − − </div></div> − ---- − <div id="6SpaceContent" class="zcontent" align="left"><div class="ZEditBox" align="justify"> <font color="#484848"><font face="Arial, sans-serif"><font size="2">'''IMPOWER'''</font></font></font><font color="#484848"><font face="Arial, sans-serif"><font size="2">(</font></font></font><font color="#484848"><font face="Arial, sans-serif"><font size="2">'''IN'''</font></font></font><font color="#484848"><font face="Arial, sans-serif"><font size="2">,</font></font></font><font color="#484848"><font face="Arial, sans-serif"><font size="2">'''N'''</font></font></font><font color="#484848"><font face="Arial, sans-serif"><font size="2">)</font></font></font> − − <font color="#484848"><font face="Arial, sans-serif"><font size="2">where IN </font></font></font><font color="#484848"><font face="Arial, sans-serif"><font size="2">is a complex number and N is the power that raise the complex number.</font></font></font> − − </div></div> − ---- − <div id="12SpaceContent" class="zcontent" align="left"> − − {| id="TABLE1" class="SpreadSheet blue" − |- class="even" − | class=" " | − | Column1 − | Column2 − | Column3 − | Column4 − |- class="odd" − | class=" " | Row1 − | class="sshl_f" | (-6.999999999999999)+(24.000000000000003)i − | class=" " | − | − | − |- class="even" − | class=" " | Row2 − | class="f52543 " | − | class="sshl_f SelectTD" | − | class="sshl_f" | − | class="sshl_f" | − |- class="odd" − | Row3 − | − | − | − | − |- class="even" − | Row4 − | − | − | − | − |- class="odd" − | class=" " | Row5 − | − | − | − | − |- class="even" − | Row6 − | − | − | − | − |} − − <div align="left">[[Image:calci1.gif]]</div></div> − ---- − <div id="7SpaceContent" class="zcontent" align="left"> − − <font color="#484848"><font face="Arial, sans-serif"><font size="2">Let's see an example.</font></font></font> − − <font color="#484848"><font face="Arial, sans-serif"><font size="2">I.e.=IMPOWER(“i+2i”,4) is -6.999+24i</font></font></font> − − </div> − ---- − <div id="9SpaceContent" class="zcontent" align="left"><div>[[Image:equation%202.gif|100%px|http://store.zcubes.com/33975CA25A304262905E768B19753F5D/Uploaded/equation%202.gif]]</div></div> − ----
Manuals/calci/IMPOWER (view source)
Revision as of 11:01, 17 December 2013
, 11:01, 17 December 2013no edit summary
<div id="16SpaceContent" align="left"><div class="ZEditBox" align="justify">
<div style="font-size:30px">'''IMPOWER(z,n)'''</div><br/>
*<math>z</math> is the complex number is of the form <math>x+iy</math>
*<math>n</math> is the power value.
==Description==
*This function gives the value of powers of complex number.
*DeMoivre's Theorem is a generalized formula to compute powers of a complex number in it's polar form.
*i'is the imaginary unit, i=sqrt(-1).
*Then the power of a complex number is defined by (z)^n=(x+iy)^n=r^n*e^inθ=r^n(cosnθ+isinnθ) where r=sqrt(x^2+y^2) and θ=tan^-1(y/x), θ∈(is belongs to) (-Pi(),Pi()].
*This formula is called DeMoivre's theorem of complex numbers.
*We can use COMPLEX function to convert real and imaginary number in to a complex number.
*In IMPOWER(z,n), n can be integer, fractional or negative.
*suppose n is nonnumeric , this function will returns the error value.
==Examples==
#IMPOWER("4+5i",3)=-235.99999+115i
#IMPOWER("9-7i",4)=-14852-8063.999999i
#IMPOWER("6",9)=10077696(EXCEL)=10077696-8i(CALCI)
#IMPOWER("i",10)=-1-16i(CALCI)=-1+6.1257422745431E-16i
*For imaginary value '0' is not accepting in CALCI.
==See Also==
*[[Manuals/calci/IMREAL | IMREAL ]]
*[[Manuals/calci/IMSUM | IMSUM ]]
*[[Manuals/calci/IMAGINARY | IMAGINARY ]]
*[[Manuals/calci/COMPLEX | COMPLEX ]]
==References==
[http://en.wikipedia.org/wiki/Binary_logarithm Binary Logarithm]