Manuals/calci/IMDIV

IMDIV(z1,z2)

$z1<math>and<math>z2<math>arecomplexnumbers.==Description==*Thisfunctiongivesthedivisionoftwocomplexnumbers.*Thisfunctionusedtoremovethe<math>i<math>(imaginaryunit)fromthedenominator.*<math>z1,z2$ are the two complex numbers in the form of $z1=a+ib$ and $z2=c+id$ , where Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle a,b,c<math> & <math>d<math> are real numbers <math>i} is the imaginary unit, $i={\sqrt {-1}}<math>.*Todothedivisionofcomplexnumberwehavefollowthesteps:step1:Wehavetowritethecomplexnumberisinthefractionform.step2:Tofindtheconjugateofthedenominator.step3:Tomutiplythenumeratoranddenominatorwithconjugate.i.e.<math>IMDIV(z1,z2)={\frac {a+ib}{c+id}}={\frac {a+ib}{c+id}}*{\frac {c-id}{c-id}}={\frac {ac+bd}{c^{2}+d^{2}}}+{\frac {(bc-ad)i}{(c^{2}+d^{2})}}$

Examples

IMDIV("4+2i","3-i")=(4+2i/3-i)*(3+i/3+i)=(12+10i+2i^2)/(3^2-i^2)=10+10i/10 (because i^2=-1)= 1+i/1=1+i
IMDIV("3-5i,2-6i")=0.9+0.2i
IMDIV("5","2+3i")=0.769-1.153i
IMDIV("1+i","2")=0.5+0.5i