Advertisements
Advertisements
प्रश्न
Find the modulus of `(1+i)/(1-i) - (1-i)/(1+i)`
उत्तर
APPEARS IN
संबंधित प्रश्न
Find the modulus and argument of the complex number `(1 + 2i)/(1-3i)`
If (x + iy)3 = u + iv, then show that `u/x + v/y =4(x^2 - y^2)`
Find the conjugate of the following complex number:
\[\frac{1}{1 + i}\]
Find the conjugate of the following complex number:
\[\frac{(3 - i )^2}{2 + i}\]
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:
\[\sqrt{3} + i\]
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:
\[\frac{1}{1 + i}\]
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:
\[\frac{- 16}{1 + i\sqrt{3}}\]
Write the conjugate of \[\frac{2 - i}{\left( 1 - 2i \right)^2}\] .
If (1+i)(1 + 2i)(1+3i)..... (1+ ni) = a+ib,then 2 ×5 ×10 ×...... ×(1+n2) is equal to.
If \[\frac{( a^2 + 1 )^2}{2a - i} = x + iy, \text { then } x^2 + y^2\] is equal to
If \[\frac{1 - ix}{1 + ix} = a + ib\] then \[a^2 + b^2\]
Solve the equation `z^2 = barz`, where z = x + iy.
If |z2 – 1| = |z|2 + 1, then show that z lies on imaginary axis.
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|.
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?
If z = x + iy lies in the third quadrant, then `barz/z` also lies in the third quadrant if ______.
