## Find the missing value when given the modulus. 2. |a-i| = √37 (in the third quadrant) I know the ans

Question

Find the missing value when given the modulus.

2.
|a-i| = √37 (in the third quadrant)

I know the answer I just need to know how to solve it!

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3 hours 2023-01-14T04:20:43+00:00 1 Answer 0 views 0

1. Solving the complex number, we get the value of the missing value that is ‘a’ = -6
We  have been given the expression as
|a – i| = √37          (1)
Which is an expression of complex number. The general expression of complex number is given as
z = x + iy
where x is the real part and iy is the imaginary part
To find the modulus value, the formula is given by,
|z| = |x + iy|
|z| = √[(real part)2 + (imaginary part)2]
|z| = √(x2 + y2)
According to the question, |z| = √37         (2)
Equating equation (1) and (2), we get
√(a2 + 1) = √37
(a2 + 1) = 37
a2 = 37 – 1
a2 = 36
a = √36
a = ±6
Now value of a can be 6 or -6. We have been given that the modulus is in third quadrant.
Hence the value will be negative. Therefore, the missing value will be -6.