PUC Science Class 11 - Karnataka Board PUC Question Bank Solutions for Mathematics

If i² = −1, then the sum i + i² + i³ +... upto 1000 terms is equal to

If \[z = \frac{- 2}{1 + i\sqrt{3}}\],then the value of arg (z) is

If a = cos θ + i sin θ, then \[\frac{1 + a}{1 - a} =\]

The principal value of the amplitude of (1 + i) is

The least positive integer n such that \[\left( \frac{2i}{1 + i} \right)^n\] is a positive integer, is.

If z is a non-zero complex number, then \[\left| \frac{\left| z \right|^2}{zz} \right|\] is equal to

If (x + iy)1/3 = a + ib, then \[\frac{x}{a} + \frac{y}{b} =\]

\[(\sqrt{- 2})(\sqrt{- 3})\] is equal to

The argument of \[\frac{1 - i\sqrt{3}}{1 + i\sqrt{3}}\] is

If \[z = \left( \frac{1 + i}{1 - i} \right)\] then z⁴ equals

If \[z = \frac{1 + 2i}{1 - (1 - i )^2}\], then arg (z) equal

\[\text { If } z = \frac{1}{(2 + 3i )^2}, \text { than } \left| z \right| =\]

\[\text { If } z = \frac{1}{(1 - i)(2 + 3i)}, \text { than } \left| z \right| =\]

\[\text { If  }z = 1 - \text { cos }\theta + i \text { sin }\theta, \text { then } \left| z \right| =\]

If \[z = \frac{1}{1 - cos\theta - i sin\theta}\] then Re (z) =

If \[x + iy = \frac{3 + 5i}{7 - 6i},\]  then y =

If θ is the amplitude of \[\frac{a + ib}{a - ib}\] , than tan θ =

If \[z = \frac{1 + 7i}{(2 - i )^2}\] , then

The amplitude of \[\frac{1}{i}\] is equal to

The argument of \[\frac{1 - i}{1 + i}\] is