Question

Find the missing value when given the modulus.

2. (picture) (in the third quadrant)

Answer 1

-6

Explanation:

I got it right on edg.

Answer 2

The value of a is -6.

Explanation:

A complex number is defined as

`z=x+iy`

`|z|=|x+iy|=√(x^2+y^2)`

where, x is real part and iy is imaginary part.

The given equation is

`|a-i|=√(37)`

Here real part is a and imaginary part is -i. So, x=a and y=-1.

`√(a^2+(-1)^2)=√(37)`

Taking square on both the sides.

`a^2+(-1)^2=37`

`a^2+1=37`

Subtract 1 from both the sides.

`a^2=36`

Taking square root on both the sides.

`a=\pm √(36)`

`a=\pm 6`

The value of a is either 6 or -6. But it is given that the picture is in third quadrant, so the value of a can not be positive.

Therefore the value of a is -6.