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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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(4 + 3i)*(3i - 4) = 4*3i - 4*4 +(3i)*(3i) - 3i*4 = 12i - 16 + 9i^2 - 12i = -16 + 9*(-1) = -16 - 9 = -25.
= +/- 5i.
ANSWER. = +/- 5i.
Thus 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.
