Question

What is the conjugate? See image below! Please help asap

1) 4- sqrt(7)
2) 8+ sqrt (-5)

Sqrt is square root, use the answers listed to the right

Answer 1

9514 1404 393

Answer:

• 2 +3i
• 8 -i√5
• 7 +2i
• 4 +√7

Explanation:

The conjugate is found by changing the sign of the square root term.‡ (For this purpose, i = √-1.)

a) the sign of 3i is changed: 2 + 3i

b) the sign of sqrt(-5) is changed: 8 -sqrt(-5) = 8 -i√5

c) the sign of 2i is changed: 7 +2i

d) the sign of sqrt(7) is changed: 4 +√7

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‡ Actually, the conjugate of a binomial is formed by changing the sign between terms. The purpose is to allow the product of the binomial and its conjugate to be the difference of squares.

Conventionally, the conjugate of a complex number is the value with the sign of the imaginary part reversed. That is why (-2i+7)* = 7+2i.