Advertisements
Advertisements
Question
Select the correct answer from the given alternatives:
If z = x + iy and |z − zi| = 1 then
Options
z lies on x-asis
z lies on y-asis
z lies on a rectangle
z lies on a circle
Advertisements
Solution
z lies on a circle
Explanation;
|z – zi| = 1 ......(given)
|x + iy – xi + y| = 1
∴ (x + y)2 + (y – x)2 = 1
∴ 2x2 + 2y2 = 1
APPEARS IN
RELATED QUESTIONS
Find the modulus and amplitude of the following complex numbers.
7 − 5i
Find the modulus and amplitude of the following complex numbers.
`sqrt(3) + sqrt(2)"i"`
Find the modulus and amplitude of the following complex numbers.
−3(1 − i)
Find the modulus and amplitude of the following complex number.
−4 − 4i
Find the modulus and amplitude of the following complex numbers.
`sqrt(3) - "i"`
If z = 3 + 5i then represent the `"z", bar("z"), - "z", bar(-"z")` in Argand's diagram
Express the following complex numbers in polar form and exponential form:
− i
Express the following complex numbers in polar form and exponential form:
`(1 + 2"i")/(1 - 3"i")`
Express the following numbers in the form x + iy:
`sqrt(3)(cos pi/6 + "i" sin pi/6)`
Express the following numbers in the form x + iy:
`"e"^((-4pi)/3"i")`
Find the modulus and argument of the complex number `(1 + 2"i")/(1 - 3"i")`
For z = 2 + 3i verify the following:
`bar((bar"z"))` = z
For z = 2 + 3i verify the following:
`"z"bar("z")` = |z|2
z1 = 1 + i, z2 = 2 − 3i. Verify the following :
`bar("z"_1 - "z"_2) = bar("z"_1) - bar("z"_2)`
z1 = 1 + i, z2 = 2 − 3i. Verify the following :
`bar("z"_1."z"_2) = bar("z"_1).bar("z"_2)`
Select the correct answer from the given alternatives:
If `-1 + sqrt(3)"i"` = reiθ , then θ = .................
Answer the following:
Find the modulus and argument of a complex number and express it in the polar form.
8 + 15i
Answer the following:
Find the modulus and argument of a complex number and express it in the polar form.
6 − i
Answer the following:
Find the modulus and argument of a complex number and express it in the polar form.
`(1 + sqrt(3)"i")/2`
Answer the following:
Find the modulus and argument of a complex number and express it in the polar form.
2i
Answer the following:
Find the modulus and argument of a complex number and express it in the polar form.
− 3i
Answer the following:
Find the modulus and argument of a complex number and express it in the polar form.
`1/sqrt(2) + 1/sqrt(2)"i"`
Answer the following:
Convert the complex numbers in polar form and also in exponential form.
z = `(2 + 6sqrt(3)"i")/(5 + sqrt(3)"i")`
Convert the complex numbers in polar form and also in exponential form.
`(-3)/2 + (3sqrt(3))/2"i"`
The polar coordinates of the point whose cartesian coordinates are (−2, −2), are given by ____________.
The modulus of z = `sqrt7` + 3i is ______
The modulus and amplitude of 4 + 3i are ______
If x + iy = `5/(3 + costheta + isintheta)`, then x2 + y2 is equal to ______
If z = `5i ((-3)/5 i)`, then z is equal to 3 + bi. The value of ‘b’ is ______.
If z = `π/4(1 + i)^4((1 - sqrt(π)i)/(sqrt(π) + i) + (sqrt(π) - i)/(1 + sqrt(π)i))`, then `(|z|/("amp"^((z))))` is equals to ______.
If A, B, C are three points in argand plane representing the complex numbers z1, z2 and z3 such that, z1 = `(λz_2 + z_3)/(λ + 1)`, where λ ∈ R, then find the distance of point A from the line joining points B and C.
