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Sagot :
Answer:
The answer is C
Step-by-step explanation:
Correct answer shown on edge
The power of 5 of complex number z is (-16√3 + 16) + 4(-√3 + 3)i
What is a complex number?
It is defined as the number which can be written as x+iy where x is the real number or real part of the complex number and y is the imaginary part of the complex number and i is the iota which is nothing but a square root of -1.
We have:
z = 1 + √3i
We have to find: z⁵
z⁵ = (1 + √3i)(1 + √3i)(1 + √3i)(1 + √3i)(1 + √3i)
z⁵ = (-2 + 2√3)(1 + √3i)(1 + √3i)(1 + √3i)
[tex]\rm z^5=\left(2\sqrt{3}-2\right)+2\left(3-\sqrt{3}\right)i(1+\sqrt{3}i)(1+\sqrt{3}i)[/tex]
[tex]\rm =\left(-4\sqrt{3}+4\right)+4\left(3-\sqrt{3}\right)i(1+\sqrt{3}i)[/tex]
z⁵ = (-16√3 + 16) + 4(-√3 + 3)i
Thus, the power of 5 of complex number z is (-16√3 + 16) + 4(-√3 + 3)i
Learn more about the complex number here:
brainly.com/question/10251853
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