Manuals/calci/IMDIV

IMDIV(ComplexNumber1,ComplexNumber2)

• 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 ComplexNumber1} and 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 ComplexNumber2} are in the form of a+bi.

Description

• This function gives the division of two complex numbers.
• This function used to remove the $i$ (imaginary unit) from the denominator.
• 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 ComplexNumber1} and 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 ComplexNumber2} are in the form of 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+ib} and 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 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} & 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 d} are real numbers 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 i} is the imaginary unit, 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 i=\sqrt{-1}} .
• Let z1 and z2 are the two Complex Numbers.
• 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.

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

• To find the Conjugate of a Complex Number we can use the function IMCONJUGATE.

ZOS Section

• The syntax is to calculate the IMDIV in ZOS is 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 IMDIV(ComplexNumber1,ComplexNumber2)} .
  • 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 ComplexNumber1} and 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 ComplexNumber2} are in the form of a+bi.
• For e.g.,IMDIV("3+2i","3-2i")

ImDiv

Examples

1. IMDIV("4+2i","3-i") =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 \frac{4+2i}{3-i}*\frac{3+i}{3+i}} = 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 \frac{12+10i+2i^2}{3^2-i^2} = 10+\frac{10i}{10}} (because 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 i^2=-1} ) = 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 1+\frac{i}{1} = 1+1i }
2. IMDIV("3-5i,2-6i") = 0.9+0.2i
3. IMDIV("5","2+3i") = 0.7692307692307693 + -1.1538461538461537i
4. IMDIV("1+i","2") = 0.5+0.5i

See Also

• COMPLEX
• IMAGINARY
• IMREAL

References

Complex Division