complex question (no pun intended) (1 Viewer)

Hermes1 · Jul 7, 2011

the cartesian equation of the locus of the point P which represents z in the argand diagram is given by:

4x + 3y = 10

hence find the minimum value of the modulus of z.

worked solution would be appreciated

Drongoski · Jul 7, 2011

Is the answer 2 ??

Hermes1 · Jul 7, 2011

thats what i got. how did u do it

Drongoski · Jul 7, 2011

If answer is correct then it's simple.

All the points z lie on the straight line given. The modulus of any point P on the line is the length of OP, O being the origin. The shortest distance is simply the perpendiculat distance from O(0,0) to P given by the 2U distance formula:

$d = \frac {|4\times 0 + 3 \times 0 - 10|}{\sqrt {(3^2 + 4^2)}} = 2$

Hermes1 · Jul 7, 2011

Drongoski said:
If answer is correct then it's simple.

All the points z lie on the straight line given. The modulus of any point P on the line is the length of OP, O being the origin. The shortest distance is simply the perpendiculat distance from O(0,0) to P given by the 2U distance formula:

$d = \frac {|4\times 0 + 3 \times 0 - 10|}{\sqrt {(3^2 + 4^2)}} = 2$

i used trig, but perp distane formula is way easier

tnx for the help

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complex question (no pun intended) (1 Viewer)

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