Question 1208826
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Perform the indicated operation and express your answer in the form a + bi.

sqrt{(4 + 3i)(3i - 4)}
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<pre>
(4 + 3i)*(3i - 4) = 4*3i - 4*4 +(3i)*(3i) - 3i*4 = 12i - 16 + 9i^2 - 12i = -16 + 9*(-1) = -16 - 9 = -25.


{{{sqrt(-25)}}} = +/- 5i.


<U>ANSWER</U>.  {{{sqrt((4+3i)*(3i-4))}}} = +/- 5i.


Thus  {{{sqrt((4+3i)*(3i-4))}}}  has two values:  one value is  5i  and  another value is  -5i.


In complete form a + bi,  first number is 0 + 5i;  the second number is 0 - 5i.


Do not be surprised: in complex domain, square root of non-zero number always has two values,
and these two values are opposite (have opposite signs).


The same as in the real domain for positive numbers.
</pre>

Solved.