Can you find the cartesian equation for the locus of points #(x, y)# if #z=x+iy# and #z+3 + z3 = 8#?
or
then with
squaring
or
By signing up, you agree to our Terms of Service and Privacy Policy
The locus of the points is an ellipse
Therefore,
Squaring both sides
Squaring both sides
This is the equation of an ellipse.
By signing up, you agree to our Terms of Service and Privacy Policy
The reqd. Locus
Respected Cesareo R. Sir has solved the Problem using
Algebraic Method. We solve it with the help Geometry.
Now, by what is given,
Enjoy Maths.!
By signing up, you agree to our Terms of Service and Privacy Policy
To find the Cartesian equation for the locus of points ((x, y)) given (z = x + iy) and (z + 3 + z  3 = 8), we'll first express (z) in terms of (x) and (y), then apply the properties of absolute value to simplify the equation.
We have (z = x + iy), so we can rewrite the given equation using this expression:
[ (x + iy) + 3 + (x + iy)  3 = 8 ]
Now, let's work with each absolute value term separately:

For (z + 3): [ (x + iy) + 3 = x + iy + 3 ]

For (z  3): [ (x + iy)  3 = x + iy  3 ]
Using the properties of absolute value, we know that (a + bi = \sqrt{a^2 + b^2}) for any complex number (a + bi). So, let's apply this property:

For (z + 3): [ x + iy + 3 = \sqrt{(x + 3)^2 + y^2} ]

For (z  3): [ x + iy  3 = \sqrt{(x  3)^2 + y^2} ]
Now, substitute these expressions back into the original equation:
[ \sqrt{(x + 3)^2 + y^2} + \sqrt{(x  3)^2 + y^2} = 8 ]
This equation represents the locus of points ((x, y)) in the Cartesian plane that satisfy the given condition. This is the Cartesian equation for the locus of points.
By signing up, you agree to our Terms of Service and Privacy Policy
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
 98% accuracy study help
 Covers math, physics, chemistry, biology, and more
 Stepbystep, indepth guides
 Readily available 24/7