Download 8.8 Complex Numbers

8.8 Complex Numbers
The complex number system enables us to take even roots of negative numbers by means of the
imaginary unit i, which is equal to the square root of –1; that is i2 = -1 and i = 1 . By
factoring –1 out of a negative expression, it becomes positive and an even root can be taken:
-b = i b . Standard form for complex expression is a + bi, where a is the real part and bi is the
imaginary part. All properties of exponents hold when the base is i, thus i1 = i, i2 = -1, i3 = i2(i)
= -1i = -i, i4 = i2(i2) = -1(-1) = 1. In general, for in, divide n by 4: if the remainder is 0, in= 1; if
the remainder is 1, in = i, if the remainder is 2, in= -1; if the remainder is 3, in= -i.
Write in a + bi form:
1. 25
2. a.  50
b. 50
3. 3 16  2
Evaluate:
4. i21
5. i39
6. i52
7. i42
Add or subtract:
5. (-1 + 6i) + (5 – 4i)
6. (-5 + i) - (-5 – i)
7. (-6 + 4i) - (2 – i) + (7 – 3i)
Multiply:
2  10
8.
9.
4(1 – 3i)
10. -5i(2 + 3i)
11. (3 - 2 i)(2 – 5i)
12. (4 + 3 i)2
13. (2 + 6i)(2 – 6i)
Divide:
14.
8
2
15.
3  5i
2i
16.
5  6i
3i