Manuals/calci/IMDIV

IMDIV(ComplexNumber1,ComplexNumber2)

• $ComplexNumber1$ and $ComplexNumber2$ 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.
• $ComplexNumber1$ and $ComplexNumber2$ are in the form of $a+ib$ and $c+id$, where $a,b,c$ & $d$ are real numbers $i$ is the imaginary unit, $i={\sqrt {-1}}$.
• 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.

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(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

• 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

Related Videos

Dividing Complex Numbers

See Also

• COMPLEX
• IMAGINARY
• IMREAL

References

Complex Division

• List of Main Z Functions

• Z3 home