5

Q1. For the complex roots of a quadratic equation, which of the following is true?

• They are always equal.
• Imaginary parts are always negatives of each other.
• Real parts are always in a ratio 1:2
• One root is always the square root of the other.

Solution

for a quadratic equation,+bx+c=0, When the discriminant  D is <0, the roots are complex given by x=where D’= -D So, the real parts of the root are same but the imaginary parts are negatives of each other.

Q2. For a complex number a+ib, a-ib is called its

• reciprocal
• conjugate
• additive inverse
• opposite

Solution

The definition of the conjugate of a complex number gives the answer.

Q3. The multiplicative inverse of 7+5i is:

• 7-5i
• (7-5i)/74
• (7+5i)/74
• (7-5i)/ 4

Solution

                                                

Q4. The product of the complex numbers 1+2i and 1-2i gives

• -3
• 8
• 5
• -5

Solution

As = -1

Q5. The multiplicative inverse of 7+5i is:

• 7-5i
• (7-5i)/74
• (7+5i)/74
• (7-5i)/ 4

Solution

                                                

Q6. The product of the complex numbers 1+2i and 1-2i gives

• -3
• 8
• 5
• -5

Solution

As = -1

Q7. The multiplicative inverse of 3 - 4i is

• 3 + 4i
• -3 + 4i
• (3 + 4i)/25
• -3 + 4i/5

Solution

Q8. For a complex number a+ib, a-ib is called its

• reciprocal
• conjugate
• additive inverse
• opposite

Solution

The definition of the conjugate of a complex number gives the answer.

Q9. The multiplicative inverse of 3 - 4i is

• 3 + 4i
• -3 + 4i
• (3 + 4i)/25
• -3 + 4i/5

Solution

Q10. For a complex number x + iy, if x > 0 and y < 0 then the number lies in the.

• First quadrant
• Second quadrant
• Third quadrant
• Fourth quadrant

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