First slide

Algebra of complex numbers

Question

If a < 0, b > 0, then $\sqrt{a} \sqrt{b}$ is equal to

Moderate

A

$- \sqrt{| a | b}$
B

$\sqrt{| a | b} i$
C

$\sqrt{| a | b}$
D

none of these

Solution

Verify by selecting particular values of a and b.
Let a = -9 and b = 4. Then
$\sqrt{a} \sqrt{b} = \sqrt{- 9} \sqrt{4} = (3 i) (2) = 6 i$
From option (1), we have
$- \sqrt{| a | b} = - \sqrt{| - 9 | \times 4} = - \sqrt{36} = - 6$
From option (2), we have
$\sqrt{| a | b} i = \sqrt{| - 9 | \times 4} i = 6 i$

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