Question

what is the conjugate of -√-5​

Answer 1

SOLUTION

TO DETERMINE

The conjugate of $- \sqrt{ - 5}$

CONCEPT TO BE IMPLEMENTED

Complex Number

A complex number z = a + ib is defined as an ordered pair of Real numbers ( a, b) that satisfies the following conditions :

(i) Condition for equality :

(a, b) = (c, d) if and only if a = c, b = d

(ii) Definition of addition :

(a, b) + (c, d) = (a+c, b+ d)

(iii) Definition of multiplication :

(a, b). (c, d) = (ac-bd , ad+bc )

Of the ordered pair (a, b) the first component a is called Real part of z and the second component b is called Imaginary part of z

If z = a + ib is a complex number

Then its conjugate is

$\sf{ \overline{z} = a - ib }$

EVALUATION

Here the given number is

$- \sqrt{ - 5}$

Above number can be rewritten as

$\sf{ - \sqrt{ - 5} }$

$\sf{ = - \sqrt{ (5 \times - 1)} }$

$\sf{ = - \sqrt{ - 1 } \times \sqrt{ 5} }$

$\sf{ = - i \sqrt{ 5} }$

Which is a complex number

Hence the required conjugate

$\sf{ = i \sqrt{ 5} }$

$\sf{ = \sqrt{ - 1} \times \sqrt{ 5} }$

$\sf{ = \sqrt{ - 5} }$

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Answer 2

Answer:

this is your answer✋✋

Step-by-step explanation:

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