College Algebra & Trigonometry, 2018a

1.4. COMPLEX NUMBERS 41
Expressing square roots of negative numbers
Square roots of negative quantities are generally expressed as a multiple of i.
Examples
√ −4=2i.
√ −25 = 5i
√ −7 ≈ 2.646i
Adding, subtracting and multiplying with complex numbers
Calculating with complex numbers has many similarities to working with variables.
The real part and imginary part are treated separately for addition and
subtraction, but can be multiplied and divided.
Examples
Compute the following:
(6 − 4i)+(−2+7i) =4+3i
(−9+2i) − (−4+6i) =−9+2i +4− 6i = −5 − 4i
3(10 + i) =30+3i
−7i(−5+8i) =35i − 56i 2
Now we encounter an interesting fact about complex numbers and, in particular,
the complex unit i. By definition, i = √ −1. Therefore, if we square i we should
get −1. In the last example problem above, we can replace the i 2 with −1 to finish
the problem.