Advertisements
Advertisements
प्रश्न
Answer the following:
Represent 1 + 2i, 2 − i, −3 − 2i, −2 + 3i by points in Argand's diagram.
Advertisements
उत्तर
The complex numbers 1 + 2i, 2 − i, − 3 − 2i, − 2 + 3i will be represented by the points A(1, 2), B(2, −1), C(−3, −2), D(−2, 3) respectively as shown below:
APPEARS IN
संबंधित प्रश्न
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 numbers.
3
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)
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:
− 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"^((-4pi)/3"i")`
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 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.
6 − i
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.
2i
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 modulus of z = `sqrt7` + 3i is ______
The modulus and amplitude of 4 + 3i are ______
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.
