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Let's look at our complex numbers in a little more detail we know that the eye comes from square rooting a negative number but what we want to deal with is a complex number which is a real number plus an imaginary one, and we identify the imaginary one by the eye which is equal to the square root of negative 1 well when we do this we always want to write it as a plus bi where an is the real part and B is the imaginary part and the eye helps us keep them apart so how would I write 2 in standard form well we recognize that 2 is purely real, so it becomes 2 and since there's no imaginary part we could write this as 2 plus 0i, and we're okay writing this just as a 2 but to show it in complex form is 2 plus 0i similarly if I have the square root of minus 36 first I reduce square root of minus 36 becomes 6i the negative becomes the square 36 is 6 and so in standard form this is called standard form a plus bi we get 0 plus 6i this is said to be purely real this is said to be purely imaginary but not all numbers do that sometimes we have a real number and an imaginary one well the real number parts easy the imaginary part that we have to simplify in this case, so this becomes 8 I notice the minus just becomes the so this then becomes -3 minus 8i, and we are now done because we have our real part minus 3 in our imaginary part minus 8i when answering problems always answer in standard form if it's purely real it's okay to write just the 2 if it's purely imaginary it's ok to write the 6i if it has both a part and an imaginary part we always list the real number part first the imaginary part second and if they are in fraction forms we always separate our fractions and reduce them separately