roots-of-complex-numbers

Roots of complex numbers

How do I find the square root of a complex number?

• The square roots of a complex number will themselves be complex:

  • i.e. if  then 

• We can then square () and equate it to the original complex number (), as they both describe :

  • 

• Then expand and simplify:

  • <img alt=”a plus b straight i equals c squared plus 2 c d straight i plus d squared straight i squared” data-mathml='<math ><semantics><mrow><mi>a</mi><mo>+</mo><mi>b</mi><mi mathvariant=”normal”>i</mi><mo>=</mo><msup><mi>c</mi><mn>2</mn></msup><mo>+</mo><mn>2</mn><mi>c</mi><mi>d</mi><mi