Upcoming SlideShare
×

# Method of completing Squares in Complex Numbers

1,405 views

Published on

A very beautiful approach for completing squares and thus finding square root of a complex number is presented

Published in: Education
2 Likes
Statistics
Notes
• Full Name
Comment goes here.

Are you sure you want to Yes No
• Be the first to comment

Views
Total views
1,405
On SlideShare
0
From Embeds
0
Number of Embeds
95
Actions
Shares
0
0
0
Likes
2
Embeds 0
No embeds

No notes for slide

### Method of completing Squares in Complex Numbers

1. 1. Method of completing squares in Complex Numbers The purpose of this slide is to show how do we complete squares in complex numbers. A very beautiful solution for finding square root of (a+ib) is also demonstrated. It is assumed that you know definition of iota and complex numbers Prepared By Parag Arora copyrights © youmarks.com
2. 2. Problem <ul><li>Find z = </li></ul><ul><li>One way to find this is by equation z to x + iy, on squaring which gives </li></ul><ul><li>7 + 24i = x 2 – y 2 + 2ixy </li></ul><ul><li>x 2 – y 2 = 7 and xy = 12 which on solving gives the value of x and y. </li></ul><ul><li>It must be emphasized here that if we visualize 7 = 4 2 – 3 2 and 12 = 4.3, we straight away get value of x and y. This is known as method of completing square. </li></ul><ul><li>The method of completing squares is shown here for a particular case. We will however generalize this method using a very beautiful approach of completing squares. </li></ul>copyrights © youmarks.com
3. 3. Finding <ul><li>Again as we did, one method is put x + iy = </li></ul><ul><li>This would as before give us </li></ul><ul><li>x 2 – y 2 =a and xy = b/2. </li></ul><ul><li>We can easily solve the above two equations and find x and y in terms of a and b. But we will present a way of completing squares for finding the roots very fast. </li></ul>copyrights © youmarks.com
4. 4. Finding <ul><li>We know that </li></ul><ul><li>( c + id ) 2 = c 2 – d 2 + 2icd. To find </li></ul><ul><li>We see that we need to figure out c and d in such a way that if cd = b/2 then c 2 – d 2 = a. </li></ul><ul><li>Let us consider the case when b > 0. Now </li></ul><ul><li>b = √b 2 </li></ul><ul><li>Or </li></ul>copyrights © youmarks.com