Manuals/calci/IMDIV

IMDIV(z1,z2)

• $z1$ and $z2$ are complex numbers.

Description

• This function gives the division of two complex numbers.
• This function used to remove the $i$ (imaginary unit) from the denominator.
• $z1,z2$ are the two complex numbers in the form of $z1=a+ib$ and $z2=c+id$, where $a,b,c$ & $d$ are real numbers $i$ is the imaginary unit, $i={\sqrt {-1}}$.
• To do the division of complex number we have follow the steps:

step 1: Write the complex number in the fraction form.
step 2: Find the conjugate of the denominator.
step 3: Multiply the numerator and denominator with conjugate.

$IMDIV(z1,z2)={\frac {a+ib}{c+id}}={\frac {a+ib}{c+id}}*{\frac {c-id}{c-id}}={\frac {ac+bd}{c^{2}+d^{2}}}+{\frac {(bc-ad)i}{(c^{2}+d^{2})}}$

Examples

1. IMDIV("4+2i","3-i") =${\frac {4+2i}{3-i}}*{\frac {3+i}{3+i}}$ = ${\frac {12+10i+2i^{2}}{3^{2}-i^{2}}}=10+{\frac {10i}{10}}$ (because $i^{2}=-1$) = $1+{\frac {i}{1}}=1+i$
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

Complex Division