Help! I'll fan and medal
Find the product of the complex number and its conjugate.
3 + 3i

A. 18
B. 9 - 9i
C. 0
D. 9 + 9i

Question

Help! I'll fan and medal
Find the product of the complex number and its conjugate.
3 + 3i

A. 18
B. 9 - 9i
C. 0
D.  9 + 9i

hatahateo · Answer

@dumbcow 
@plainntall 
@welshfella 
@wkep1234

plainntall · Answer

So we have the complex number 3+3i
what is its conjugate?

hatahateo · Answer

9-9i?

plainntall · Answer

No, the conjugate of a+bi is a-bi, you just change the sign of the imaginary part.  So what is the conugate of 3+3i?

hatahateo · Answer

3-3i

plainntall · Answer

right, now we need to find the product of (3+3i)(3-3i)

hatahateo · Answer

18

mww · Answer

Simple rule for these

If z is the complex number a + ib and z' is its conjugate a - ib
Then their product is always a real number given by the square of the modulus!

$$zz' = (a+ib)(a-ib) = a^2 - i^2b^2 = a^2 + b^2 = |z|^2$$

plainntall · Answer

Yes!  :D

hatahateo · Answer

Thanks guys! Can you help me with one more? I'm a little confused, I'll open another question