If $A = (3 - 4 i)$ and $B = (9 + k i)$ , where $k$ is a constant.
If $A B - 15 = 60$ , then the value of $k$ is

6

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12

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Solution

The correct option is B $12$

Given, $A = 3 - 4 i, B = 9 + k i, A b - 15 = 0$

$∴ A B = (3 - 4 i) (9 + k i)$

$∴ 27 + 3 k i - 36 i - 4 k i^{2} - 15 = 60$

$∴ - 48 + 3 k i - 36 i + 4 k = 0$

Separate the real and imaginery part equal to zero, then we get the value of $k$ ,

$∴ - 48 + 4 k = 0, 3 k - 36 = 0$

$∴ - 48 = - 4 k, 3 k = 36$

$∴ k = 12, k = 12$

So, the value of $k$ is $12$ .

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If A=(3−4i) and B=(9+ki), where k is a constant. If AB−15=60, then the value of k is

The correct option is B 12 Given, A=3−4i,B=9+ki,Ab−15=0 ∴AB=(3−4i)(9+ki) ∴27+3ki–36i–4ki2−15=60 ∴−48+3ki−36i+4k=0 Separate the real and imaginery part equal to zero, then we get the value of k, ∴−48+4k=0,3k–36=0 ∴−48=−4k,3k=36 ∴k=12,k=12 So, the value of k is 12.

If $A = (3 - 4 i)$ and $B = (9 + k i)$ , where $k$ is a constant.
If $A B - 15 = 60$ , then the value of $k$ is