Answer

Verified

437.1k+ views

Hint: Divide and multiply a number so that the complex number can be expressed in terms of sine & cosine of angles.

Lets say, $x = 1 + i\sqrt 3$

Multiply and divide the RHS of the above equation with $2$.

$

x = 2\left( {\dfrac{{1 + i\sqrt 3 }}{2}} \right) = 2\left( {\dfrac{1}{2}} \right) + 2\left( {\dfrac{{i\sqrt 3 }}{2}} \right) \\

x = 2\cos \dfrac{\pi }{3} + i2\sin \left[ {\dfrac{\pi }{3}} \right] \\

$

This above equation can be written in exponential form

As we know $\cos \theta + i\sin \theta = {e^{i\theta }}$

Doing the same in the equation obtained we get,

$x = 2{e^{i\dfrac{\pi }{3}}}$

Hence, $2{e^{i\dfrac{\pi }{3}}}$ in modulus amplitude form.

Note :- In these types of questions we have to obtain the given equation in the form of $\cos \theta + i\sin \theta = {e^{i\theta }}$ to convert it into modulus amplitude form. We should also be aware of trigonometric values needed to convert the equation in general form.

Lets say, $x = 1 + i\sqrt 3$

Multiply and divide the RHS of the above equation with $2$.

$

x = 2\left( {\dfrac{{1 + i\sqrt 3 }}{2}} \right) = 2\left( {\dfrac{1}{2}} \right) + 2\left( {\dfrac{{i\sqrt 3 }}{2}} \right) \\

x = 2\cos \dfrac{\pi }{3} + i2\sin \left[ {\dfrac{\pi }{3}} \right] \\

$

This above equation can be written in exponential form

As we know $\cos \theta + i\sin \theta = {e^{i\theta }}$

Doing the same in the equation obtained we get,

$x = 2{e^{i\dfrac{\pi }{3}}}$

Hence, $2{e^{i\dfrac{\pi }{3}}}$ in modulus amplitude form.

Note :- In these types of questions we have to obtain the given equation in the form of $\cos \theta + i\sin \theta = {e^{i\theta }}$ to convert it into modulus amplitude form. We should also be aware of trigonometric values needed to convert the equation in general form.

Recently Updated Pages

Assertion The resistivity of a semiconductor increases class 13 physics CBSE

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths

How do you arrange NH4 + BF3 H2O C2H2 in increasing class 11 chemistry CBSE

Is H mCT and q mCT the same thing If so which is more class 11 chemistry CBSE

What are the possible quantum number for the last outermost class 11 chemistry CBSE

Is C2 paramagnetic or diamagnetic class 11 chemistry CBSE

Trending doubts

What is BLO What is the full form of BLO class 8 social science CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Difference Between Plant Cell and Animal Cell

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Fill the blanks with proper collective nouns 1 A of class 10 english CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

What organs are located on the left side of your body class 11 biology CBSE

What is pollution? How many types of pollution? Define it