complexx (1 Viewer)

[jnney]

Solve z^4+16i=0

 

[seanieg89]

 

[bleakarcher]

z^4+16i=0
=>z^4=-16i=16cis(-pi/2)
Let z=rcis(θ).
Now, [rcis(θ)]^4=r^4cis(4θ)=16cis[(-pi/2)+2kpi] for k=0,1,2,3,...
Hence, r=2 and θ=(-pi/8)+(kpi/2)
:.z=2cis(-pi/8), 2cis(3pi/8), 2cis(7pi/8), 2cis(-5pi/8)

 

[SpiralFlex]

I recall correctly this question is from Harry's. It has the incorrect answer at the back. These roots do not appear as conjugates.

 

[Sanical]

You can do it via complex roots of unity except having it with 16i.

Otherwise, you can factorise it via difference of two squares. EDIT: Oops, you can't do that unless it's a real number =/.

In any case, you ask a lot of questions lol. You should get a tutor to answer all these.

 

[jnney]

I recall correctly this question is from Harry's. It has the incorrect answer at the back. These roots do not appear as conjugates.

oh! okay

 

[SpiralFlex]

Also,

oh! okay

Several people asked me and we came to the conclusion the answers were definitely wrong.

 

[lolcakes52]

I recall correctly this question is from Harry's. It has the incorrect answer at the back. These roots do not appear as conjugates.

The roots are not conjugates though? The coefficient of z^0 is imaginary.

 

[asianese]

All complex roots occur in conjugates. It's part of the fundamental theorem of algae.

 

[nightweaver066]

All complex roots occur in conjugates. It's part of the fundamental theorem of algae.

Only true if the coefficients are real (conjugate root theorem).

 

[lolcakes52]

All complex roots occur in conjugates. It's part of the fundamental theorem of algae.

Really? I couldn't find anything on the fundemental of algae..http://en.wikipedia.org/wiki/Algae

Anyway, the fundamental theorem of algebra says that any polynomial of nth degree has exactly n complex zeroes. Nothing about conjugates.

 

[SpiralFlex]

Really? I couldn't find anything on the fundemental of algae..http://en.wikipedia.org/wiki/Algae

Anyway, the fundamental theorem of algebra says that any polynomial of nth degree has exactly n complex zeroes. Nothing about conjugates.

...

 

[Carrotsticks]

Really? I couldn't find anything on the fundemental of algae..http://en.wikipedia.org/wiki/Algae

Anyway, the fundamental theorem of algebra says that any polynomial of nth degree has exactly n complex zeroes. Nothing about conjugates.

Rote learner detected. Destroy.

 

[lolcakes52]

All complex roots occur in conjugates. It's part of the fundamental theorem of algae.

This is what i was referring to, it was a joke guys. Calm down lol