Difference between revisions of "Manuals/calci/IMDIV"

Revision as of 05:06, 24 April 2014

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.

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 .
- $ComplexNumber1$ and $ComplexNumber2$ are in the form of a+bi.
For e.g.,IMDIV("3+2i","3-2i")

Examples

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 $i^{2}=-1$ ) = $1+{\frac {i}{1}}=1+i$
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

References

Complex Division

@@ Line 1: / Line 1: @@
-<div style="font-size:30px">'''IMDIV(z1,z2)'''</div><br/>
+<div style="font-size:30px">'''IMDIV(ComplexNumber1,ComplexNumber2)'''</div><br/>
-*<math>z1</math> and <math>z2</math> are complex numbers.
+*<math>ComplexNumber1</math> and <math>ComplexNumber2</math> are in the form of a+bi.
 ==Description==
 *This function gives the division of two complex numbers.
 *This function used to remove the <math>i</math> (imaginary unit) from the denominator.
-*<math>z1,z2</math> are the two complex numbers in the form of <math>z1=a+ib</math> and <math>z2=c+id</math>, where <math>a,b,c</math> & <math>d</math> are real numbers <math>i</math> is the imaginary unit, <math>i=\sqrt{-1}</math>.
+*<math>ComplexNumber1</math> and <math>ComplexNumber2</math> are in the form  of <math>a+ib</math> and <math>c+id</math>, where <math>a,b,c</math> & <math>d</math> are real numbers <math>i</math> is the imaginary unit, <math>i=\sqrt{-1}</math>.
+*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.
-:<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)}</math>
+:<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)}</math>.
+*To find the Conjugate of a Complex Number we can use the function [[Manuals/calci/IMCONJUGATE  | IMCONJUGATE]].
+==ZOS Section==
+*The syntax is to calculate the IMDIV in ZOS is <math>IMDIV(ComplexNumber1,ComplexNumber2)</math>.
+**<math>ComplexNumber1</math> and <math>ComplexNumber2</math> are in the form of a+bi.
+*For e.g.,IMDIV("3+2i","3-2i")
 ==Examples==

Difference between revisions of "Manuals/calci/IMDIV"

Revision as of 05:06, 24 April 2014

Contents

Description

ZOS Section

Examples

See Also

References

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