Linear Algebra

Question

What is the multiplicative inverse of the complex number 0.2∠0.3

Answer 1

I assume the 0.3 is radians.

 

z = 0.2 e^0.3i

 

1/z = 1 / (0.2 e^0.3i) = (1/0.2) e^-0.3i

 

1/z = 5 e^-0.3i

 

Test the solution:  Is z * 1/z = 1 ?

 

z * 1/z = (0.2 e^0.3i)(5 e^-0.3i) = (0.2* 5)e^{i(3i - 3i)} = 1 e⁰ = 1