Complex number technique: ‘Taking out half power’

‘Taking out half power’ is a useful technique to simplify the division of complex numbers.

Example 1

Write down the five roots of the equation w5=1

Hence show that the roots of the equation Tex2Img_1405327571 are Tex2Img_1405327808 where Tex2Img_1405327849

Solution

Tex2Img_1405327984

Therefore

Tex2Img_1405328069

2w-wz=2+z

2(w-1)=z(w+1)

Tex2Img_1405328177

Tex2Img_1405328778

Tex2Img_1405329158 (Taking out half power)

Tex2Img_1405329321

=Tex2Img_1405327808 where Tex2Img_1405327849 (proved)

Example 2

complex 2015

Example 3

Capture

‘Taking out half power” only works when the coefficient of both terms are the same in absolute terms. If it isn’t, then have to use another technique: Multiply by conjugate

1 thought on “Complex number technique: ‘Taking out half power’

Leave a Reply

Please log in using one of these methods to post your comment:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out /  Change )

Google photo

You are commenting using your Google account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s

%d bloggers like this: