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If |z| = 4 and arg z = (5π/6), then the value of z is
  • a)
    2√3 - 2i
  • b)
    2√3 + 2i
  • c)
    -2√3 + 2i
  • d)
    -√3 + i
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
If |z| = 4 and arg z = (5π/6), then the value of z isa)2√3 - ...
Given Information:
|z| = 4
arg z = 5π/6

Solution:

Step 1: Finding the Real and Imaginary Parts
We can express z in polar form as z = r(cosθ + isinθ), where r = |z| and θ = arg z.
Here, r = 4 and θ = 5π/6.
So, z = 4(cos(5π/6) + isin(5π/6)).

Step 2: Calculating the Trigonometric Functions
cos(5π/6) = -√3/2 and sin(5π/6) = 1/2.

Step 3: Substituting Values to Find z
Substitute the values of cos(5π/6) and sin(5π/6) into the polar form of z:
z = 4(-√3/2 + i/2)
z = -2√3 + 2i
Therefore, the value of z is -2√3 + 2i, which corresponds to option 'c'.
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If |z| = 4 and arg z = (5π/6), then the value of z isa)2√3 - 2ib)2√3 + 2ic)-2√3 + 2id)-√3 + iCorrect answer is option 'C'. Can you explain this answer?
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