Question

Find the product of the complex number and its conjugate.
1 + 3i

A. 1 + 9i

B. 10

C. -8

D. 1 - 9i

Answer 1

i thought it was D. but i just want to see if im right or not?

Answer 2

It is not D. Did you multiply it out using the FOIL method?
(1 + 3i)(1 - 3i) = ?

Answer 3

oh no i didnt.. hmm ..

Answer 4

\[(a+bi)(a-bi)=a^2+b^2\] a real number
don't think about \(i\) and don't think about minus signs, just straight up \(a^2+b^2\)

Answer 5

would it be 10?

Answer 6

and i might add no foil

Answer 7

Yes , the answer is 10.

Answer 8

yes, \(1^2+3^2=1+9=10\)

Answer 9

thank you!!

Answer 10

would either of you know how to do this problem;

Find the real numbers x and y that make the equation true.
-3 + yi = x + 6i

Answer 11

Hint: If y = 6 then the imaginary terms cancel.

Answer 12

so would
y= 6
x= -3

Answer 13

Sure! In any equation, left side equals to the right side iff each component on one side of the equation equals to its corresponding component on the other side.

Answer 14

@katherinekc Yes, you are right.

Answer 15

Therefore if you have two complex numbers equal to each other then the real part of the complex number on one side equals to the real part of the other complex number on the other side of the equation, and the imaginary part of the complex number on one side equals to the imaginary part of the complex number on the other side of the equation.

Answer 16

so then id be correct when saying
y= 6
x= -3

Answer 17

The real parts on both sides are -3 and x. Therefore x = -3.

The imaginary parts on both sides are yi and 6i. Therefore y = 6.

Therefore you are one hundred percent correct @katherinekc! Great work!

Answer 18

thankyou!!

Answer 19

Of Course! You deserve it!