Algebra and solid Exam 2017 model
(1)
page(2)
Q(5) In the opposite figure: If Z1 and Z2 and Z1 Z2 are complex numbers then Z2 =
c e
d f
-2i i
-i
Y
Z1Z2
Z1
X
2i
1 πi Z 1Z 2 re (2 π +θ )i 2 = = e = cos π + i sin π = i Z2 = θi 2 2 Z1 re
()
1
Q(6)
c e
()
If the point (-2,4,m) lies on the sphere
(X + 2)2 + (Y − 1)2 + (Z − 3 )2 = 25
then one value of m=….
d f
6 7
3 + (m − 3 ) = 25 2
2
∴m - 3 = 4
8 9
∴m = 7
Q(7) If ω is an imaginary cube root of unity then (1 + ω − ω2 ) = …… 7
c e
128 ω -128 ω
(− 2ω )
2 7
d f
128 ω2 -128 ω2
= −128ω 4 = −128ω 2
Q(8) If A = (1, 2, -4), B = (1, 1, k - 1) and || A + B || = 7 unit of length then k = ............................
c e
-1,11 1,11
{-1,11}
d f
-11,-1 1,12