Answer:
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
