Find the product of the complex number and its conjugate.

Question

1. 2- 3i

 

2. -3 + 4i

 

3. -1 - √2i

Answer 1

For a complex number a + bi, the conjugate is a - bi.

 

1.  For 2 - 3i, the conjugate is 2 - (-3i) = 2 + 3i

 

(2-3i)(2+3i) = 4 + 6i - 6i - 9i² = 4 + 9 = 13          [Use the FOIL method]

 

Note that the product is always a real number.

 

2.  For -3 + 4i, the conjugate is -3 - 4i

 

(-3+4i)(-3-4i) = __________

 

3.  Can you do #3 on your own?

Answer 2

(2-3i)(2+3i)=4-9i²=4-(9)(-1)=4+9=13

(-3+4i)(-3-4i)=9-16i²=9-(16)(-1)=9+16=25

(-1-√2i)(-1+√2i)=1-2i²=1-(2)(-1)=1+2=3