Square Root of a Complex Number
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Q.
If , then
Q.
Find the square root of the following complex numbers :
(i) -5 + 12 i
(ii) -7 - 24i
(iii) 1 - i
(iv) - 8 - 6i
(v) 8 - 15i
(vi) -11 - 64 √−1
(vii) 1 + 4 √−3
(viii) 4i
(ix) - i
Q.
Write the values of the square root of -i.
Q.
Relative R in the set N of natural numbers defined as R={(x, y):y=x+5andx<4}
enter 1-Reflexive
2-Symmetric
3-Transitive
4-Equivalence
5-None
Determine whether the following relation is reflexive, symmetric and transitive
enter 1-Reflexive
2-Symmetric
3-Transitive
4-Equivalence
5-None
Q. ω is an imaginary cube root of unity. If (1+ω2)m=(1+ω4)m then least positive integral value of m is
- 6
- 5
- 4
- 3
Q. If (3+x2008+x2009)2010=a0+a1x+a2x2+…+anxn,
then the value of
a0−12a1−12a2+a3−12a4−12a5+a6− ⋯upto n terms is
then the value of
a0−12a1−12a2+a3−12a4−12a5+a6− ⋯upto n terms is
- 32010
- 1
- 22010
- 42010
Q. If z2+z+1=0, where z is complex number, then the value of (z+1z)+(z2+1z2)+(z3+1z3)+⋯+(z6+1z6) is
Q.
If 1, ω, ω2 are the three cube roots of unity, then for α, β, γ, δϵR, the expression (α+βω+γω2+δω2β+αω2+γω+δω) is
1
ω
−ω
ω−1
Q. If (1+i1−i)m/2=(1+ii−1)n/3=1, (m, n∈N), then the greatest common divisor of the least values of m and n is
Q.
Write formula.
Q. If f(x)=1−2x+3x2−4x3+⋯+17x16−18x17, then the coefficient of x15 in f(x−1) is/are
- 16⋅ 18C16−17⋅ 18C17
- 18C17−18 18C16
- 19C17−19 18C16
- 17⋅ 18C16−16⋅ 19C16
Q.
If z=(i)i, where i=√−1, then Re(z) is: