Find the modulus and argument of the complex number -16/1+i√3
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Given:
The complex number -16/1+i√3
To find:
Find the modulus and argument of the complex number -16/1+i√3
Solution:
From given, we have,
The complex number -16/1+i√3
⇒ -16 + i√3
The modulus of a complex number is given as follows.
|z| = √[a² + b²]
|z| = √[(-16)² + (√3)²]
|z| = √[256+3]
|z| = 16.09
The argument of a complex number is given as follows.
tan ∅ = b/a
tan ∅ = √3/-16
∅ = tan^{-1} [√3/-16]
∅ = 180 - 6.178
∅ = 173.8 °
Therefore, the modulus and argument of the complex number -16/1+i√3 is 16.09 and 173.8 ° respectively.
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