Question

Which of the following is the conjugate of a complex number with 5 as the real part and −2i as the imaginary part?

5 + 2i
−5 − 2i
−5 + 2i
5 − 2i

Answer 1

The conjugate of a + bi is a - bi.
The conjugate of a - bi is a + bi.
All you do is change the sign of the imaginary part.

The conjugate of 5 - 2i is 5 + 2i.
The 5 remains the same. The imaginary part -2i becomes +2i.

Answer 2

Option A is correct.

The conjugate of a complex number 5 -2i is, 5 + 2i

Explanation:

The complex number is an element (a, b) of the Cartesian plane.

Every element of the plane is a linear combination of the two vectors, 1 and i.

i.,e
`(a, b) = a+ib`

If we think of a point in the plane as a complex number, we always write a + bi.

A real number a is called the real part and bi is the imaginary part of
`a+ib`

As per the given statement:

real part = 5

Imaginary part = -2i

then, the complex number (z)=
`5 -2i`

To find the conjugate of the complex number 5-2i.

Complex conjugate states that a complex number is the number with an equal real part and an imaginary part equal in magnitude but opposite in sign.

then;

Conjugate of complex number (i.e 5-2i) = 5 + 2i