Advertisements
Advertisements
प्रश्न
Find the modulus and amplitude of the following complex numbers.
`sqrt(3) + sqrt(2)"i"`
Advertisements
उत्तर
Let z = `sqrt(3) + sqrt(2)"i"`
∴ a = `sqrt(3)`, b = `sqrt(2)`, i.e. a > 0, b > 0
∴ |z| = `sqrt("a"^2 + "b"^2)`
= `sqrt((sqrt(3))^2 + (sqrt(2))^2`
= `sqrt(3 + 2)`
= `sqrt(5)`
Here, `(sqrt(3), sqrt(2))` lies in 1st quadrant.
∴ amp (z) = `tan^-1("b"/"a")`
= `tan^-1(sqrt(2)/sqrt(3))`
= `tan^-1(sqrt(2/3))`
APPEARS IN
संबंधित प्रश्न
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"`
Find the modulus and amplitude of the following complex numbers.
1 + i
Find the modulus and amplitude of the following complex numbers.
(1 + 2i)2 (1 − i)
Express the following complex numbers in polar form and exponential form:
− i
Express the following complex numbers in polar form and exponential form:
`1/(1 + "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:
`sqrt(2)(cos (7pi)/4 + "i" sin (7pi)/4)`
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"^((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")` = |z|2
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)`
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 arg(z) = θ, then arg `bar(("z"))` =
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.
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.
`(-1 - "i")/sqrt(2)`
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.
Answer the following:
Convert the complex numbers in polar form and also in exponential form.
z = `(2 + 6sqrt(3)"i")/(5 + sqrt(3)"i")`
Answer the following:
Convert the complex numbers in polar form and also in exponential form.
z = `-6 + sqrt(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 ______
For all complex numbers z1, z2 satisfying |z1| = 12 and |z2 - 3 - 4i| = 5, the minimum value of |z1 - z2| 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 ______.
