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This mock test of Test: Complex Number- 1 for Quant helps you for every Quant entrance exam.
This contains 5 Multiple Choice Questions for Quant Test: Complex Number- 1 (mcq) to study with solutions a complete question bank.
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QUESTION: 1

If a,b (a≠b), are the real roots of the equation (k + 1)(x^{2 }+ x + 1)^{2 }+ (k - 1)(x^{4 }+ x^{2 }+ 1) = 0, k ≠ 1, 0.

Then the product of the roots is

Solution:

Since the equation (x^{2 }+ x + 1) = 0 . oes not have any real roots, the roots of the original equation will be the root of the equation (kx^{2} + x + k) = 0

Hence product of the roots = k/k = 1

QUESTION: 2

Polar form of a complex number is

Solution:

QUESTION: 3

|z_{1} + z_{2} | =

Solution:

|*z*1 + *z*2|= .

|*z*1| + |*z*2|= .

We have to prove that

is true.

Square both sides.

Square both sides again.

2*x*_{1}*x*_{2}*y*_{1}*y*_{2} ≦ *x*_{1}^{2}*y*_{2}^{2 }+ *y*_{1}^{2}*x*_{2}^{2} and we get

0 ≦ (*y*_{1}*x*_{2} - *x*_{1}*y*_{2})^{2}.

It is true because *x*_{1,} *x*_{2}, *y*_{1}, *y*_{2} are all real.

QUESTION: 4

|z_{1} - z_{2} | =

Solution:

QUESTION: 5

A^{2} + b^{2}

Solution:

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### Solved Examples - Complex Number

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