Advertisements
Advertisements
Question
Express the following numbers in the form x + iy:
`"e"^((5pi)/6"i")`
Solution
z = reiθ = `"e"^((5pi)/6"i")`
∴ r = 1, θ = `(5pi)/6`
Polar form of z = r(cos θ + i sin θ)
= `1(cos (5pi)/6 + "i" sin (5pi)/6)`
= `cos(pi - pi/6) + "i" sin(pi - pi/6)`
= `-cos pi/6 + "i" sin pi/6`
= `-sqrt(3)/2 + "i"* 1/2`
= `-sqrt(3)/2 + 1/2"i"`
APPEARS IN
RELATED QUESTIONS
Find the modulus and amplitude of the following complex numbers.
−3(1 − i)
Find the modulus and amplitude of the following complex numbers.
−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 + "i"sqrt(3)`
Find the modulus and amplitude of the following complex numbers.
(1 + 2i)2 (1 − 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:
`-1 + sqrt(3)"i"`
Express the following complex numbers in polar form and exponential form:
−1
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"^((-4pi)/3"i")`
Find the modulus and argument of the complex number `(1 + 2"i")/(1 - 3"i")`
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.
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.
`1/sqrt(2) + 1/sqrt(2)"i"`
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 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.
