#### Complex Numbers Two Marks Questions

12th Standard EM

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Maths

Time : 00:45:00 Hrs
Total Marks : 30
15 x 2 = 30
1. If z=x+iy, find the following in rectangular form.
$Re\left( \cfrac { 1 }{ z } \right)$

2. Represent the complex number −1−i

3. Write the following in the rectangular form:
$\cfrac { 10-5i }{ 6+2i }$

4. Find the square roots of −6+8i

5. Obtain the Cartesian form of the locus of z=x+iy in
$\overline { z } =2^{ -1 }$

6. Show that the following equations represent a circle, and, find its centre and radius
|3z-6+12i|=8

7. Write in polar form of the following complex numbers
$3-i\sqrt { 3 }$

8. Simplify the following:
i i2i3...i40

9. Find the modulus and principal argument of the following complex numbers.
$-\sqrt { 3 } +i$

10. Represent the complex numbe $1+i\sqrt { 3 }$ in polar form.

11. Find Re (z) and im (z) if z = 5i11 + 7i3

12. If (cosθ + i sinθ)2 = x + iy, then show that x2+y2 =1

13. If 1, ω, ω2 are the cube roots of unity show that (1+ω2)3 - (1+ω)3 =0

14. Find the argument of -2

15. Find the values of the real number x and y if 3x + (2x - 3y) i = 6 + 3i9.