Complex Number

Printable View

January 25th 2010, 11:53 AM
BabyMilo

Complex Number

which topics does complex number come under as?

anyway.

$\begin{vmatrix} z-(3+3i)=2 \end{vmatrix}$

$\Rightarrow \begin{vmatrix} (x-3)+(y-3)i\end{vmatrix}=2 $

$= (x-3)^2+(y-3)^2=2^2$

then it asks find the max and min of $\begin{vmatrix} z \end{vmatrix}$

thanks!
January 25th 2010, 12:03 PM
Jhevon

Quote:

Originally Posted by BabyMilo

which topics does complex number come under as?

anyway.

$\begin{vmatrix} z-(3+3i)=2 \end{vmatrix}$

$\Rightarrow \begin{vmatrix} (x-3)+(y-3)i\end{vmatrix}=2 $

$= (x-3)^2+(y-3)^2=2^2$

then it asks find the max and min of $\begin{vmatrix} z \end{vmatrix}$

thanks!

you should post the problem in its entirety.

you could solve for $\sqrt{x^2 + y^2}$ , you would get it as a function of x and y and you minimize and maximize that. but that requires calc 3. so too much work.

another way is to let geometry help you. if you graphed what's happening in the complex plane, you would notice that z must lie on the circle of radius 2 centered at (3,3). draw a line from the origin passing through (3,3) cutting right across the circle. the length of the line segment from the origin to the first place the line cuts the circle is the min |z|, add the diameter of the circle to that, that is, add 4, and you get the max |z|

(by the way, | is a symbol found on your keyboard. hold down shift and press \)
January 25th 2010, 12:06 PM
BabyMilo

Quote:

Originally Posted by Jhevon

you should post the problem in its entirety.

you could solve for $\sqrt{x^2 + y^2}$ , you would get it as a function of x and y and you minimize and maximize that. but that requires calc 3. so too much work.

another way is to let geometry help you. if you graphed what's happening in the complex plane, you would notice that z must lie on the circle of radius 2 centered at (3,3). draw a line from the origin passing through (3,3) cutting right across the circle. the length of the line segment from the origin to the first place the line cuts the circle is the min |z|, add the diameter of the circle to that, that is, add 4, and you get the max |z|

(by the way, | is a symbol found on your keyboard. hold down shift and press \)

im bad at geometry as well XD...seriously not joking.

how do i find out the min or caluclate?
January 25th 2010, 12:12 PM
BabyMilo

Quote:

Originally Posted by Jhevon

you should post the problem in its entirety.

you could solve for $\sqrt{x^2 + y^2}$ , you would get it as a function of x and y and you minimize and maximize that. but that requires calc 3. so too much work.

another way is to let geometry help you. if you graphed what's happening in the complex plane, you would notice that z must lie on the circle of radius 2 centered at (3,3). draw a line from the origin passing through (3,3) cutting right across the circle. the length of the line segment from the origin to the first place the line cuts the circle is the min |z|, add the diameter of the circle to that, that is, add 4, and you get the max |z|

(by the way, | is a symbol found on your keyboard. hold down shift and press \)

would it be $\sqrt {3^2+3^2}-2$ ?
January 25th 2010, 12:14 PM
Jhevon

1 Attachment(s)

Quote:

Originally Posted by BabyMilo

im bad at geometry as well XD...seriously not joking.

how do i find out the min or caluclate?

it's not as hard as you may think. i have attached a very suggestive diagram. think about how you would do it.

min |z| = OA

max |z| = OB
January 25th 2010, 12:16 PM
Jhevon

Quote:

Originally Posted by BabyMilo

would it be $\sqrt {3^2+3^2}-2$ ?

for min |z|, yes. of course, you can simplify this

see, not so bad, right?
January 25th 2010, 12:27 PM
BabyMilo

Quote:

Originally Posted by Jhevon

for min |z|, yes. of course, you can simplify this

see, not so bad, right?

what does it simplify to? $3\sqrt{2}-2$ ?

but shouldnt it be in the form of a+bi

since y=imaginary and x=real

thanks for your time.

so the final answer would be? min(1.59,1.59) (3sf)?
January 25th 2010, 12:34 PM
Jhevon

Quote:

Originally Posted by BabyMilo

what does it simplify to? $3\sqrt{2}-2$ ?

yes

Quote:

but shouldnt it be in the form of a+bi

since y=imaginary and x=real

no, |z| is a real number. it is the modulus of z, which is a magnitude.

Quote:

so the final answer would be? min(1.59,1.59) (3sf)?

as mentioned above, |z| is a real number, not a coordinate. and do not use decimals, leave your answer exact as you did above