I assume you mean (5 - 10i) squared; just multiply it by itself, in other words:(5 - 10i)(5 - 10i)
To multiply two binomials, you need to multiply each term on the left by each term on the right (four terms in total). Remember that i squared = -1.
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(5 - 10i)²
= (5 - 10i)(5 - 10i)
= 5² - 5×10i - 5×10i + (10i)²
= 25 - 100i + 100×(√-1)²
= 25 - 100i - 100
= -75 - 100i
Yes, they do. If a+bi is a solution, a-bi is also a solution.
The codomain of a function is an arbitrary set that contains all the images of a function. Thus, the function defined by f(x) = cos x + i sin x might be said to have codomain C, or the set of all complex numbers. The range is much more specific: it is the set of all the images, and nothing more. In this case, the range is {a + bi = z in C: |z| = 1}.