introduction-to-complex-numbers

Cartesian form of complex numbers

Complex numbers are a set of numbers which contain both a real part and an imaginary part. The set of complex numbers is denoted as .

What is an imaginary number?

• Up until now, when we have encountered an equation such as we would have stated that there are “no real solutions” as the solutions are  which are not real numbers

• To solve this issue, mathematicians have defined one of the square roots of negative one as ; an imaginary number

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• We can use the rules for manipulating surds to manipulate imaginary numbers.

• We can do this by rewriting surds to be a multiple of  using the fact that <img alt=”square root of a b end root equals square root of a cross times square root of b” data-mathml='<math ><semantics><mrow><msqrt><mi>a</mi><mi>b</mi></msqrt><mo>=</mo><msqrt><mi>a</mi>&