Science (English Medium) कक्षा ११ - CBSE Question Bank Solutions for Mathematics

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:

\[\sqrt{3} + i\]

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:

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

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 z₁, z₂ and z₃, z₄ 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 \[\frac{2 - i}{\left( 1 - 2i \right)^2}\] .

Evaluate the following:

¹⁴C₃

Evaluate the following:

¹²C₁₀

Evaluate the following:

³⁵C₃₅

Evaluate the following:

^n + 1C_n

Evaluate the following:

If (1+i)(1 + 2i)(1+3i)..... (1+ ni) = a+ib,then 2 ×5 ×10 ×...... ×(1+n²) is equal to.