Air Force X Group Complex Number| सम्मिश्र संख्या

Maths By Bhagwati Sir

Q1. The value of (1+i)5 is

(a) -8

(b) 8i

(c) 8

(d) 32

Q2. If x − iy = √𝑎−𝑖𝑏

𝑐−𝑖𝑑 then find the value of (x²+y²)²

;fn x − iy = √𝑎−𝑖𝑏

𝑐−𝑖𝑑 rks (x²+y²)² dk eku gksxk\

(a) 𝑎2+𝑏2

𝑐2+𝑑²

(b) 𝑎2−𝑏2

𝑐2−𝑑²

(c) 𝑐2+𝑑²

𝑎2+𝑏²

(d) 𝑐2−𝑑²

𝑎2+𝑏²

Q3. Find the modulus of 1+𝑖

1−𝑖−

1−𝑖

1+𝑖

1+𝑖

1−𝑖−

1−𝑖

1+𝑖 dk ekikad D;k gS

(a) 1

(b) 2

(c) -1

(d) -2

Q4. If x + iy =𝑎+𝑖𝑏

𝑎−𝑖𝑏 find the value of x²+y²

(a) 1

(b) 0

(c) -1

(d) 2

Q5. If and are imaginary cube roots of unity then

4 +

4 +1

is

;fn o bdkbZ ds lfEeJ ewy gS rks 4 +

4 +1

dk eku gSA

(a) 3

(b) 0

(c) 1

(d) 2

Q6. If 𝑧 =3+𝑖

3−𝑖 The find amplitude of z is

;fn 𝑧 =3+𝑖

3−𝑖 rks z dk dks.kkad D;k gksxk

(a) 𝜋

2

(b) 𝜋

3

(c) 𝜋

6

(d) 𝜋

4

Q7. If 1+2𝑖

2+𝑖= 𝑟 (𝑐𝑜𝑠 + 𝑖 𝑠𝑖𝑛) then

(a) 𝑟 = 1, = tan−1 3

4

(b) 𝑟 = 5 = tan−1 4

3

(c) 𝑟 = 1, = tan−1 4

3

(d) N.O.T

Q8. If z=x+iy satisfie amp (z-1)=amp (z+3i) then the

value of (x-1) : y is equal to

;fn z=x+iy amp (z-1)=amp (z+3i) dks lUrq’V djrk gS rks (x-1)

: y dk eku gksxk

(a) 2 : 1

(b) 1 : 3

(c) – 1: 3

(d) 2 : 3

Q9. If is an imaginary cube root of uniy then

(1 + 𝜔 − 𝜔2)7 equals

;fn bdkbZ dk ?kuewy gS rks (1 + 𝜔 − 𝜔2)7 dk eku D;k gksxkA

(a) 128

(b) -128

(c) 128²

(d) -128²

Q10. If is a cube root of unity then find (1-) (1-²)

(1+4) (1+8)

;fn bdkbZ dk ?kuewy gS rks (1-) (1-²) (1+4) (1+8) dk eku

gSA

(a) 0

(b) 1

(c) 2

(d) 3

Q11. If is cube root unity find 1

(

1+2+32

2+3+2 ) +

(2+3+𝑤2

3++22 )1

²

Q12. |𝑧−1

𝑧+11| = 1 represent.

(a) Circle

(b) Straight line

(c) an ellips

(d) Hyperbola

Q13. |𝑧−3𝑖

𝑧+3𝑖| = 1 represent.

(a) Circle

(b) Straight line

(c) an ellips

(d) Hyperbola

Q14. If 1, , ² be cube roots of unity, then (1-+²)5

+ (1+-²)5 = ?

(a) 4

(b) 8

(c) 16

(d) 32

Q15. If 1, , ² be cube roots of unity, then (1+)3 –

(1+)3 = ?

(a) 2

(b) -2

(c) 0

(d) 2

Q16. If 1, , ² be cube roots of unity, then (1-+²)

(1-²+4) (1-4+8)… to 2n factors is equal to:

(a) 2n

(b) 22n

(c) 0

(d) 1

Q17. If 3=1 and ≠1, then 𝑎+𝑏+𝑐²

𝑐+𝑎+𝑏²+

𝑎+𝑏+𝑐²

𝑏+𝑐+𝑎²=?

(a) 2

(b) -2

(c) 1

(d) -1

Q18. If x=a+b, y=a+b² and z= a²+b, then

(x3+y3+z3) is equal to:

(a) 3(a3+b3)

(b) 3abc

(c) a3+b3+c3

(d) 0

Q19. If 1, , ² be cube roots of unity, then the

value of (2+5+2²)6 is

(a) 576

(b) 625

(c) 729

(d) None

Q20. If 1, , ² be cube roots of unity, then the (2-)

(2-²) (2-10)(2-11) is (a) 49

(b) 36

(c) 56

(d) None

Q21. If 1, , ² are cube roots of unity, then 𝑎+𝑏+𝑐

𝑏+𝑐+𝑎²=?

(a)

(b) ²

(c) 1

(d) None

Q22. (−1+𝑖3

2)

17

+ (−1−𝑖3

2)

17

=? (a) 1

(b) -1

(c) 0

(d) None