## Complex Number and Quadratic Equations Quiz-18

Complex numbers and quadratic equations is a segment of maths that deals with crucial theorems and concepts along with various formulae. It comprises of linear and quadratic equations along with roots related to the complex number's set (known as complex roots)..

Q1.  Consider the equation 10z2-3iz-k=0, where z is a complex variable and i2=-1. Which of the following statements is true?
•  For real positive numbers k, both roots are purely imaginary
•  For all complex numbers k, neither root is real
•  For real purely imaginary numbers k, both roots are real and irrational
•  For real negative numbers k, both roots are purely imaginary
Solution
Q2. The expression [(1+sin⁡〖Ï€/8+i cos⁡〖Ï€/8〗 〗)/(1+sin⁡〖Ï€/8-i cos⁡〖Ï€/8〗 〗 )]8=
•  1
•  -1
•  i
•  -i
Solution

Q3. If roots of x2-(a-3)x+a=0 are such that at least one of them is greater than 2, then
•  a∈[7,9]
•  a∈[7,∞]
•  a∈[9,∞]
•  a∈[7,9)
Solution

Q4. If a,b,c are three distinct positive real numbers, then the number of real roots of ax2+2b|x|-c=0 is
•  0
•  4
•  2
•  None of these
Solution

Q5. If i=√(-1), then 4+5[(-1/2)+i√3/2]334+3[(-1/2)+(i√3/2)]365 is equal to
•  1-i√3
•  -1+i√3
•  i√3
•  -i√3
Solution

Q6. The smallest positive integer n for which [(1+i)/(1-i)]n = 1 is
•  n=8
•  n=16
• n=12
•  None of these
Solution

Q7. If x,y and z are real and different and u=x2+4y2+9z2-6yz-3zx-2xy, then u is always
•  Non-negative
•  Zero
•  Non-positive
•  None of these
Solution

Q8. If the ratio of the roots of ax2+2bx+c=0 is same as the ratio of the px2+2qx+r=0, then
•  2b/ac=q2/pr
•  b/ac=q/pr
•  b2/ac=q2/pr
•  None of these
Solution

Q9.  If one root of x2-x-k=0 is square of the other, then k=
•  2±√5
•  2±√3
•  3±√2
•  5±√2
Solution
Q10. If n∈N>1 then sum of real part of roots of zn=(z+1)n is equal to
•  n/2
•  (n-1)/2
•  -n/2
• (1-n)/2
Solution

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