CBSE Math 11 Practice Paper 04

CBSE 11 Mathematics

Practice Paper 04 

1. If x + iy = \(\frac{a + ib}{a - ib}\), prove that \(x^2 + y^2 = 1\).

2. If \(x - iy =\sqrt\frac{a - ib}{c - id}\) prove that \((x^2+y^2)^2=\frac{a^2 + b^2}{c^2 + d^2}\).

3. If \(z_1 = 2 – i, z_2 = 1 + i\), find \(|\frac{z_1 + z_2 + 1}{z_1 - z_2 + 1}|\).

4. Express each of the complex number given in the form a + ib. 

    (a)  \((5i)(\frac{-1}{5} i)\)

    (b)  \(i^9+i^19\)

    (c)  \(i^-39\)

    (d)  \( (\sqrt3+\sqrt-2)\)\((2\sqrt3-i)\)

    (e)  \(\frac{5+\sqrt2 i}{1-\sqrt2 i}\)

5. Find the multiplicative inverse of each of the complex numbers 

    (a)  \(4–3i\) 

    (b)  \(\sqrt5 + 3i\) 

    (c)  \(– i\)

6.  Prove that \(Re(z_1z_2)=Rez_1Rez_2-Imz_1-Imz_2\).

7.  If \((a+ib)^2=x+iy\) Prove that \((a^2+b^2)^2=x^2+y^2\).

8.  Find the value of \(1+i^2 + i^4 + i^6 + i^8 + ---- + i^100\).

9.  Solve for x and y, \(3x + (2x-y) i= 6 – 3i\).

10.  Let \(z_1 = 2 – i, z_2 = -2+i\) Find \(Re \frac{(z_1z_2)}{z_1}\)

11. Find the conjugate and the modulus of each of the following

      (a)  \(3-\sqrt3 i\)

      (b)  \((2+2i)^2\)

      (c)  \(\frac{2+\sqrt3 i}{3-2i}\)

      (d)  \(\frac{4}{3-4i}\)

      (e)  \((3+\sqrt5 i)^2\)

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