Complex Numbers and Quadratic Equations

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

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In z=4+i, what is the real part?

4 i 1 4+i

(x+3) + i(y-2) = 5+i2, find the values of x and y.

x=8 and y=4 x=2 and y=4 x=2 and y=0 x=8 and y=0

If z1 = 2+3i and z2 = 5+2i, then find sum of two complex numbers.

4+8i 3-i 7+5i 7-5i

If a + ib = c + id, then

a2 + c2 = 0 b2 + c2 = 0 b2 + d2 = 0 a2 + b2 = c2 + d2

The value of arg (x) when x < 0 is

0 π/2 π none of these

If 1 – i, is a root of the equation x2 + ax + b = 0, where a, b ∈ R, then the value of a – b is

-4 0 2 1

The least value of n for which {(1 + i)/(1 – i)}n is real, is

1 2 3 4

Let z be a complex number such that |z| = 4 and arg(z) = 5π/6, then z =

-2√3 + 2i 2√3 + 2i 2√3 – 2i -√3 + i

If ω is an imaginary cube root of unity, then (1 + ω – ω²)7 equals

128 ω -128 ω 128 ω² -128 ω²

0+0i is ______________________for complex number z.

Additive inverse

Additive identity element

Multiplicative identity element

Multiplicative inverse

The value of 1 + i2 + i4 + i6 + … + i2n, is

Positive

Negative

Cannot be evaluated

If a complex number z lies in the interior or on the boundary of a circle of radius 3 units and centre (– 4, 0), the greatest value of |z +1| is

Let z1 and z2 be two roots of the equation z² + az + b = 0, z being complex. Further assume that the origin, z1, and z1 form an equilateral triangle. Then,

a² = b

a² = 2b

a² = 3b

a² = 4b

The curve represented by Im(z²) = k, where k is a non-zero real number, is

A pair of straight line

An ellipse

A parabola

A hyperbola

Value of I (IoT),is ____________.

-1

(-1)1/2