HSC Science (Electronics) ११ वीं कक्षा - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

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)

Find real values of θ for which `((4 + 3"i" sintheta)/(1 - 2"i" sin theta))` is purely real.

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:

− i

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 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: 

`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")`

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")`

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