English

Find the modulus and amplitude of the following complex numbers. 3 - Mathematics and Statistics

Advertisements
Advertisements

Question

Find the modulus and amplitude of the following complex numbers.

3

Sum
Advertisements

Solution

Let z = 3 = 3 + 0i.

∴  a = 3, b = 0

∴ z is a real number, it lies on the positive real axis.

∴ |z| = `sqrt(a^2 + b^2)`

= `sqrt(3^2 + 0^2)`

= `sqrt(9 + 0)`

= 3

and amp (z) = 0.

shaalaa.com
Argand Diagram Or Complex Plane
  Is there an error in this question or solution?
Chapter 1: Complex Numbers - Exercise 1.3 [Page 15]

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.

−8 + 15i


Find the modulus and amplitude of the following complex numbers.

−3(1 − i)


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 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 numbers in the form x + iy: 

`sqrt(2)(cos  (7pi)/4 + "i" sin  (7pi)/4)`


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:

`bar((bar"z"))` = z


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:

If `-1 + sqrt(3)"i"` = re , then θ = ................. 


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.

`(-1 - "i")/sqrt(2)`


Answer the following:

Find the modulus and argument of a complex number and express it in the polar form.

− 3i


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"`


Convert the complex numbers in polar form and also in exponential form.

`(-3)/2 + (3sqrt(3))/2"i"`


The modulus and amplitude of 4 + 3i are ______


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.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×