Question

(1+2i)/(2-3i) Solve

Answer 1

Explain.

Answer 2

To simplify a complex fraction you take the denominator and determine what is called the conjugate surd. This denominator is 2-3i, the conjugate surd is the real value unchanged but change the sign of the imaginary value. So the conjugate surd is 2+3i.

Then you multiply both the numerator and denominator by this conjugate sure.

1+2i 2+3i
-------------------
2-3i 2+3i

Note this does not change the value of the fraction as we are effectively multiplying by 1.

2+3i+4i+6i^2
-------------
4+6i-6i-9i^2

consolidate similar terms
2+7i+6i^2
----------
4-9i^2

Remember that i^2 is actually a minus 1 (-1)

-4+7i
-------
13