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2 answers:
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We have to calculate the fourth roots of this complex number:
We start by writing this number in exponential form:
Then, the exponential form is:
The formula for the roots of a complex number can be written (in polar form) as:
Then, for a fourth root, we will have n = 4 and k = 0, 1, 2 and 3.
To simplify the calculations, we start by calculating the fourth root of r:
<em>NOTE: It can not be simplified anymore, so we will leave it like this.</em>
Then, we calculate the arguments of the trigonometric functions:
We can now calculate for each value of k:
Answer:
The four roots in exponential form are
z0 = 18^(1/4)*e^(i*π/8)
z1 = 18^(1/4)*e^(i*5π/8)
z2 = 18^(1/4)*e^(i*9π/8)
z3 = 18^(1/4)*e^(i*13π/8)
we are given points as
(-2,-4)
(0,2)
(1,5)
we can points
and then we can join them
After that we can get idea about it's shape
we can see that
this is straight line
so, this is linear model
Hence, option-C................Answer
