Complex numbers 4u (1 Viewer)

[jnney]

Find the square roots of:

1. 2-root5i


2. i

 

[jnney]

Can i please get a reply

 

[Alkanes]

Happy to help but may take a long time for a noob like me

 

[Shadowdude]

Find the square roots of:

1. 2-root5i


2. i

For 2:

Let z = (a+bi)
So: z^2 = (a^2 - b^2)+2abi

Equate real and imaginary parts, solve the simultaneous equations.


Done!


Someone else soon will do a full solution, but that's the general principle for these simple ones.

 

[nightweaver066]

Guessing what you mean in the first question is:


That can be represented as:


So:


Expanding RHS and equate real coefficients and unreal coefficients:


and


Rearrange the second equation and sub it in to the first:







Sub an x value in to and solve to get y

Do the same for the other x value to get the other y value.

Put in the form both answers in the form x + iy and you have your answer for that.

Can someone check if i'm doing this right.. I'm new to this too.

 

[Alkanes]

Let =

Therefore, 2-root5i =

=

Thus, and



=


= 3


Now,



Solve simultaneously x = and y =

Hence =


Someone please check, my solutions looks wrong.. and to OP i skipped a few steps cos i cbf, so it may look confusing

 

[UnrealAnchovies]

is nightweaver yr11?

 

[SpiralFlex]

is nightweaver yr11?

All of them above are Year 11 except Shadowdude.

 

[jnney]

And for rooti=a+bi?

 

[Alkanes]

Give it a go first. Btw was my solution correct?

 

[funnytomato]

Let =

Therefore, 2-root5i =

=

Thus, and



=


= 3


Now,



Solve simultaneously x = and y =

Hence =


Someone please check, my solutions looks wrong.. and to OP i skipped a few steps cos i cbf, so it may look confusing

3rd last line
y^2=1/2

 

[funnytomato]

And for rooti=a+bi?

sqrt(i)=a+bi
i=a^2-b^2+2abi

equating real and imaginary parts (0+i=a^2-b^2+2abi)
a^2=b^2 (1)
2ab=1 (2)

express one variable in terms of the other, either a or b from 2
sub into 1, then you have a reducible quadratic
hopefully you know the rest of it

don't be so stressed out about 4u maths, you're still in year11

 

[michaeljennings]

its good to get a headstart on 4u though if you are in year eleven, gives you a huge advantage over the rest of your peers if youre willing to work hard and put in the effort in yr 11

 

[Hermes1]

yeah definitely. what michael said. its great to get a headstart. i wish i had done it.

 

[michaeljennings]

yeah biggest regret of yr 11 was not getting a headstart on 4u and not improving the standard of the essays i was writing for english