Consider the complex number z = a + bi.
i. write z in polar form. what do the variables represent?
ii. if r = 3 and theta = 90°, where would z be plotted in the complex plane?
iii. use the conditions in part (ii) to write z in rectangular form. explain how this representation corresponds
to the location of z that you found in part (ii).

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step-by-step explanation:

a, b, c, d are correct.

step-by-step explanation:

we have g(x) = 3 and are required to find which option is a translation of g(x).

now, 'translation' is a transformation which means to shift the function in any direction and the general form of translation is g(x) + k, where k is any real number.

so, according to the options we see that all are correct as they satisfy the general form of translation.

also, it can be seen from the graph below that the function g(x) = 3 is shifted from its position in all the four options.