Help with complex solution of z, polar form and z plane
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Help with complex solution of z, polar form and z plane

[From: ] [author: ] [Date: 12-06-06] [Hit: ]
Regards,Dragon.......
z= 4+j3
using Pythagoreans theorem, r or |z| = 5
sin Θ = b/r = 3/5 = 0.75

/////// Here's where I'm confused /////////

0.75 = 36 ° 52'

I'm not sure how my teacher came to that conclusion, can someone point me in the right direction or show me the conversion process.

-
Hello,

When you have a complex z=a+ib
|z| = √(a² + b²)
Arg|z| = θ      such as cos(θ)=a/|z| and sin(θ)=b/|z|

So in your case:
z = 4 + 3i
|z| = √(4² + 3²) = √(16 + 9) = √25 = 5
sin(θ) = 3/5  and cos(θ) = 4/5

Then
θ = sin⁻¹(3/5) = cos⁻¹(4/5) ≈ 36.86° ≈ 36° 52'

The errors in your description:
3/5 ≠ 0.75
You obviously forgot "sin⁻¹" and "cos⁻¹"

Regards,
Dragon.Jade :-)
1
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