20/4/25
COMPLEX NUMBERS
1) i⁹¹=?
a) -1 b) 1 c) i d) - i
2) i²²⁶=?
a) -1 b) 1 c) i d) - i
3) i²⁷³=?
a) i b) -i c) 1 d) - 1
4) i¹²⁴ =?
a) -1 b) 1 c) i d) - i
5) i⁻⁷⁵
a) 1 b) -1 c) i d) - i
6) i⁻³⁸=?
a) i b) - i c) 1 d) - q
7) For any positive integer n, (- √-1)⁴ⁿ⁺³=?
a) 1 b) -1 c) i d) - i
8) If I= √-1 and n is a positive integer then (iⁿ + iⁿ⁺¹+ iⁿ⁺²+ iⁿ⁺³)=?
a) I b) iⁿ c) 1 d) 0
9) (i¹⁰⁹ + i¹¹⁴ + i¹¹⁹ + i¹²⁴)=?
a) 0 b) I c) -2i d) 2
10) 3i³⁴ + 5i²⁷ - 2i³⁸ + 5i⁴¹ =?
a) 1 b) -1 c) - 4i d) 10i
11) If a and b are integers then √a x √b = √(ab) is true only when
a) a and b are both positive
b) a and b are both negative
c) a and b are both zero
d) atleast one of a and b is non-negative
12) √-9 x √-25=?
a) 15 b) -15 c) 15i d) -15i
13) Which of the following statements is correct?
a) (5+ 7i)> (3+ 4i)
b) (5+ 7i)< (3+ 4i)
c) (3+ 4i)> (4+ 3i)
d) none
14) Which of the following statements is correct?
a) 3i> 2i b) 1+ 3i> 2i c) i> 0 d) none
15) Which of the following statements is correct?
a) (2+ 3i)> (2- 3i)
b) (3+ 2i)> (-3+ 2i)
c) (5+ 4i)> (-5- 4i) d) none
16) {(1- i)/(1+ i)}²=?
a) 1 b) -1 c) -1/2 d) 1/√2
17) If (a + ib)= √{(1+ i)/(1- i)} then the value of (a² + b²) is
a) 1 b) -1 c) 2 d) -2
18) The smallest positive integer n for which {( + i)/(1- i)}ⁿ= 1 is
a) 2 b) 3 c) 4 d) 6
19) If (a² + b²)= 1 then (1+ b + ia)/(1+ b - ia)=?
a) (a+ ib) b) (b + ia) c) i(a + b) d) none
20) (1+2i)/(1- i) lies in
a) quadrant I
b) quadrant II
c) quadrant III
d) quadrant IV
21) if (x + iy)= {(a+ ib)/(c + id)} then (x² + y²)=?
a) (a²+ b²)/(c² + d²) b) (a²- b²)/(c² + d²) c) (a²+ b²)/(c² - d²) d) none
22) (1+ i)⁻¹= ?
a) (2- i) b) (-1/2 + i/2) c) (1/2 - i/2) d) none
23) (1- 2i)⁻²= ?
a) (3/25 - 4i/25)
b) (- 3/25 + 4i/25)
c) (-3/25 - 4i/25) d) none
24) (1- i)⁻³=?
a) (1/4 - i/4)
b) (-1/4 + i/4)
c) (-1/4 - i/4) d) none
25) (2- 3i)(-3+ 4i)=?
a) (6+ 17i) b) (6- 17i) c) (-6+ 17i) d) none
26) (3- 5i)÷ (-2+ 3i)=?
a) (21/13 - i/13)
b) (-21/13 - i/13)
c) (21/13 + i/13) d) none
27) If (2- √-9)/(1- √-4)= (x + iy) then
a) x= 2/5, y= 3/5
b) x= 2/5, y= 2/5
c) x= 8/5, y= 1/5 d) none
28) (1- √-1)(1+ √-1)(5- √-7)(5+ √-7)=?
a) (25+ 7i) b) (32+ 5i) c) (29 - 3i) d) none
29) The multiplicative inverse of (-2+ 5i) is
a) (-2/29 + 5i/29)
b) (2/29 - 5i/29)
c) (-2/29 - 5i/29)
d) (2/29 + 5i/29)
30) The multiplicative inverse of (3+ 2i)² is
a) (-5/159 + 12i/169)
b) (5/159 - 12i/169)
c) (5/159 + 12i/169) d) none
31) The complex number z such that |(z - i)/(z + i)|= 1 lies on
a) the x-axis b) the line y=1 c) a circle d) none
32) The complex number z such that |(z - 5i)/(z + 5i)|= 1 lies on
a) the x-axis b) the y-axis c) a circle d) none
33) The complex number z such that|(z -2)/(z +2)|= 2 lies on
a) the x-axis b) the y-axis c) a circle d) none
34) -2, when expressed in polar form, is
a) -2(cos π/2 + i sin π/2)
b) -2(cos π + i sin π)
c) 2(cos 2π + i sin 2π) d) none
35) -3i, when expressed in polar form, is
a) 3(cos (-π/2) + i sin (-π/2))
b) 3(cos π/2 + i sin π/2)
c) -3(cos π/2 + i sin π/2) d) none
36) (1+ i), when expressed in polar form, is
a) 2(cos π/2 + i sin π/2)
b) 2(cos π/4 + i sin π/4)
c) √2(cos π/4 + i sin π/4) d) none
16/3/25
1) Write down the following statements in set-theoretical notations
a) 3 is an element of a set A.
b) 4 does not belong to a set B.
c) C is a set of D.
d) P and Q are disjoints sets.
2) Represent the following sets in tabular (or Roster) form:
a) set a factors of 30.
b) X={a: a is a perfect square and 2 < a≤ 49}.
c) Y={x: x is an even natural number greater than 20}.
3) Write the following sets in the set-builder form:
a) set of letters in the word 'statistics'.
b) A= {3,6,9, 12,15,...}.
c) Set of integers either equal or greater than 3 but less than 25.
9/3/25
a) i²⁵³. i
b) (1+ i)² + (1- i)².
c) ω³⁷
2) Express (1+ 3i)/(2- 5i) in the form x + iy , Where x, y are real.
3) If x = 1+ i and y= 1- i, find the value of x²+ xy+ y².
4) If ³√(x + it) = 2+ 3i, find the value of x + 5y.
5) Find the conjugate of :
1/(3+ i).
6) Find the modulus of :
(1+ 2i)/(2- i).
7) Express in modulus -amplitutude form:
1+ i.
8) Find the square roots of :
5 - 12i.
9) if one imaginary cube root of 1 be ω, show that
a) (aω + b + ω²)/(bω²+ a + ω) = ω.
b) (1- 2ω + ω²)(1- 2ω²+ ω)= 9.
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