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 (syntax error): {\displaystyle a,b,c<math> & <math>d<math> are real numbers <math>i} is the imaginary unit, <math>i=\sqrt{-1}<math>.
• To do the division of complex number we have follow the steps:

step 1: We have to write the complex number is in the fraction form.
step 2: To find the conjugate of the denominator.
step 3: To mutiply the numerator and denominator with conjugate.

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

1. 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
2. IMDIV("3-5i,2-6i")=0.9+0.2i
3. IMDIV("5","2+3i")=0.769-1.153i
4. IMDIV("1+i","2")=0.5+0.5i

See Also

• COMPLEX
• IMAGINARY
• IMREAL

References

Exponential function