Answer:
17+6i
-----------
25
Step-by-step explanation:
2+3i
---------
4+3i
We want to multiply by the complex conjugate of the denominator
4+3i has a complex conjugate of 4-3i
2+3i 4-3i
--------- * --------------
4+3i 4-3i
Lets multiply the numerator
(2+3i) ( 4-3i)
2*4 +4*3i -3i*2 - 3i*3i =
8 +12i -6i - 9i^2
Remember i^2 = -1
8 +6i -9(-1)
17 +6i
Lets multiply the denominator
(4+3i) ( 4-3i)
4*4 +4*3i -3i*4 - 3i*3i =
16 +12i -12i - 9i^2
Remember i^2 = -1
16 -9(-1)
25
Putting numerator over denominator
17+6i
-----------
25
