Question

The product of (3 - 4i) and ____ is 25.

Answer 1

( 3 + 4i )

Explanation:

For this problem, we need to know that i^2 = -1. With this, let's solve the multiplication problem.

So to get rid of the i, we know it needs to be squared. The question is, for the sun of the products do we have a -4i or a +4i? So we will test both.

( 3 - 4i )^2 ?= 25

( 3 - 4i )( 3 - 4i ) ?= 25

9 - 12i - 12i - 16 ?= 25

We can stop here since we know that 24i will never equal 25.

So let's try the -4i

( 3 + 4i )( 3 - 4i ) ?= 25

9 + 12i - 12i + 16 ?= 25

9 + 16 ?= 25

25 == 25

Thus, our term for this to be true is ( 3 + 4i ).

Cheers.