Qwertyuiop[]
Junior Member
- Joined
- Jun 1, 2022
- Messages
- 123
Hi, I have to find the modulus and the arg of this complex number: 1+i tanθ1I started by writing this in the general/algebraic form.
After multiplying the numerator and denominator with conjugate and simplifying i get: cos2θ−isinθcosθThen a=cos2θb=−sinθcosθSo the modulus is (cos2θ)2+(cosθsinθ)2 which simplifies to cosθ
To find the argument of z, we learned this formula cosθ=∣z∣a;sinθ=∣z∣b
using this i get : cosθ=cosθandsinθ=−sinθ
cos theta is positive and sin theta is negative therefore it must be in the 4 quadrant so i wrote arg(z) as an inequality 0≤arg(z)≤−2πIs the answer for mod(z) and arg(z) correct?
After multiplying the numerator and denominator with conjugate and simplifying i get: cos2θ−isinθcosθThen a=cos2θb=−sinθcosθSo the modulus is (cos2θ)2+(cosθsinθ)2 which simplifies to cosθ
To find the argument of z, we learned this formula cosθ=∣z∣a;sinθ=∣z∣b
using this i get : cosθ=cosθandsinθ=−sinθ
cos theta is positive and sin theta is negative therefore it must be in the 4 quadrant so i wrote arg(z) as an inequality 0≤arg(z)≤−2πIs the answer for mod(z) and arg(z) correct?