Find the conjugate and product of the following surds

2i + 9
-2i + 1
-3 + iy

The conjugate of 2i + 9 = -2i + 9

Product of (2i+9) and (2i+9)  is 36i + 77

Step-by-step explanation:

Given - 2i + 9

To find - Find the conjugate and product of the following surds

Proof -

We know that,

The sum and difference of two simple quadratic surds are said to be conjugate surds to each other.

To find a complex conjugate, simply change the sign of the imaginary part (the part with the i ).

So,

The conjugate of 2i + 9 = -2i + 9

Now,

Product of surd (2i+9) is

(2i+9)(2i+9) = 2i(2i) + 2i(9) + 9(2i) + 9(9)

                  = 4i² + 18i + 18i + 81

                  = -4 + 36i + 81          { because i² = -1 }

                  = 77 + 36i

⇒Product of (2i+9) and (2i+9)  is 36i + 77

1. x> -5

2. x< 8

step-by-step explanation:

1. 2x> -10

divide by 2 from both sides of equation.

2x/2> -10/2

simplify, to find the answer.

-10/2=-5

x> -5 is the correct answer.

2. 3x< 24

divide by 3 from both sides of equation.

3x/3< 24/3

simplify, to find the answer.

24/3=8

x< 8 is the correct answer.

i hope this you, and have a wonderful day!

0.50 , 0.75

step-by-step explanation: