Advertisements
Advertisements
प्रश्न
Answer the following:
Find the modulus and argument of a complex number and express it in the polar form.
6 − i
उत्तर
Let z = 6 − i
∴ a = 6, b = − 1, a > 0, b < 0
∴ |z| = r
= `sqrt("a"^2 + "b"^2)`
= `sqrt(6^2 + (-1)^2)`
= `sqrt(36 + 1)`
= `sqrt(37)`
Here (6, −1) lies in 4th quadrant
∴ amp (z) = θ = `2pi + tan^-1 ("b"/"a")`
= `2pi + tan^-1 ((-1)/6)`
∴ the polar form of z = r(cos θ + i sin θ)
= `sqrt(37)(cos theta + "i" sin theta)`
where θ = `2pi + tan^-1 (-1/6)`
APPEARS IN
संबंधित प्रश्न
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.
`sqrt(3) - "i"`
Find the modulus and amplitude of the following complex numbers.
3
Find the modulus and amplitude of the following complex numbers.
`1 + "i"sqrt(3)`
Find real values of θ for which `((4 + 3"i" sintheta)/(1 - 2"i" sin theta))` is purely real.
Express the following complex numbers in polar form and exponential form:
`-1 + sqrt(3)"i"`
Express the following complex numbers in polar form and exponential form:
`(1 + 2"i")/(1 - 3"i")`
Express the following complex numbers in polar form and exponential form:
`(1 + 7"i")/(2 - "i")^2`
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:
`7(cos(-(5pi)/6) + "i" sin (- (5pi)/6))`
Express the following numbers in the form x + iy:
`"e"^(pi/3"i")`
Express the following numbers in the form x + iy:
`"e"^((-4pi)/3"i")`
Express the following numbers in the form x + iy:
`"e"^((5pi)/6"i")`
Convert the complex number z = `("i" - 1)/(cos pi/3 + "i" sin pi/3)` in the polar form
For z = 2 + 3i verify the following:
`bar((bar"z"))` = z
For z = 2 + 3i verify the following:
`"z" - bar"z"` = 6i
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)`
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:
The modulus and argument of `(1 + "i"sqrt(3))^8` are respectively
Select the correct answer from the given alternatives:
If `-1 + sqrt(3)"i"` = reiθ , then θ = .................
Select the correct answer from the given alternatives:
If z = x + iy and |z − zi| = 1 then
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.
`(1 + sqrt(3)"i")/2`
Answer the following:
Find the modulus and argument of a complex number and express it in the polar form.
`(-1 - "i")/sqrt(2)`
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:
Represent 1 + 2i, 2 − i, −3 − 2i, −2 + 3i by points in Argand's diagram.
The modulus of z = `sqrt7` + 3i is ______
For all complex numbers z1, z2 satisfying |z1| = 12 and |z2 - 3 - 4i| = 5, the minimum value of |z1 - z2| is ______.
If z = `5i ((-3)/5 i)`, then z is equal to 3 + bi. The value of ‘b’ is ______.
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.
