Advertisements
Advertisements
Question
Answer the following:
Represent 1 + 2i, 2 − i, −3 − 2i, −2 + 3i by points in Argand's diagram.
Advertisements
Solution
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
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.
−8 + 15i
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"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
Express the following complex numbers in polar form and exponential form:
`1/(1 + "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:
`7(cos(-(5pi)/6) + "i" sin (- (5pi)/6))`
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")`
Find the modulus and argument of the complex number `(1 + 2"i")/(1 - 3"i")`
For z = 2 + 3i verify the following:
`"z"bar("z")` = |z|2
For z = 2 + 3i verify the following:
`("z" + bar"z")` is real
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)`
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.
8 + 15i
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"`
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 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 ______.
