मराठी

Find the Modulus and Argument of the Complex Number (1 + 2i)/(1-3i) - Mathematics

Advertisements
Advertisements

प्रश्न

Find the modulus and argument of the complex number `(1 + 2i)/(1-3i)`

 
बेरीज

उत्तर

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 5: Complex Numbers and Quadratic Equations - Miscellaneous Exercise [पृष्ठ ११३]

APPEARS IN

एनसीईआरटी Mathematics [English] Class 11
पाठ 5 Complex Numbers and Quadratic Equations
Miscellaneous Exercise | Q 13 | पृष्ठ ११३

व्हिडिओ ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्‍न

Find the real numbers x and y if (x – iy) (3 + 5i) is the conjugate of –6 – 24i.


Find the modulus  of  `(1+i)/(1-i) - (1-i)/(1+i)`


Find the conjugate of the following complex number:

4 − 5 i


Find the conjugate of the following complex number:

\[\frac{1}{3 + 5i}\]


Find the conjugate of the following complex number:

\[\frac{(3 - i )^2}{2 + i}\]


Find the conjugate of the following complex number:

\[\frac{(1 + i)(2 + i)}{3 + i}\]


Find the conjugate of the following complex number:

\[\frac{(3 - 2i)(2 + 3i)}{(1 + 2i)(2 - i)}\]


Find the modulus of \[\frac{1 + i}{1 - i} - \frac{1 - i}{1 + i}\].


Find the modulus and argument of the following complex number and hence express in the polar form:

1 − i


Find the modulus and argument of the following complex number and hence express in the polar form:

\[\frac{1 - i}{1 + i}\]


Find the modulus and argument of the following complex number and hence express in the polar form:

\[\frac{1 + 2i}{1 - 3i}\]


Find the modulus and argument of the following complex number and hence express in the polar form:

 sin 120° - i cos 120° 


Find the modulus and argument of the following complex number and hence express in the polar form:

 \[\frac{- 16}{1 + i\sqrt{3}}\]


If z1z2 and z3z4 are two pairs of conjugate complex numbers, prove that \[\arg\left( \frac{z_1}{z_4} \right) + \arg\left( \frac{z_2}{z_3} \right) = 0\].


Write the conjugate of \[\frac{2 - i}{\left( 1 - 2i \right)^2}\] .


If \[\frac{( a^2 + 1 )^2}{2a - i} = x + iy, \text { then } x^2 + y^2\] is equal to


If \[x + iy = (1 + i)(1 + 2i)(1 + 3i)\],then x2 + y2 =


Solve the equation `z^2 = barz`, where z = x + iy.


If a complex number z lies in the interior or on the boundary of a circle of radius 3 units and centre (–4, 0), find the greatest and least values of |z + 1|.


If a complex number lies in the third quadrant, then its conjugate lies in the ______.


If z1 = `sqrt(3) + i  sqrt(3)` and z2 = `sqrt(3) + i`, then find the quadrant in which `(z_1/z_2)` lies.


What is the conjugate of `(sqrt(5 + 12i) + sqrt(5 - 12i))/(sqrt(5 + 12i) - sqrt(5 - 12i))`?


Solve the system of equations Re(z2) = 0, z = 2.


State True or False for the following:

If z is a complex number such that z ≠ 0 and Re(z) = 0, then Im(z2) = 0.


If `(a^2 + 1)^2/(2a - i)` = x + iy, what is the value of x2 + y2?


sinx + icos2x and cosx – isin2x are conjugate to each other for ______.


If z = x + iy lies in the third quadrant, then `barz/z` also lies in the third quadrant if ______. 


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×