SOLUTION: Find the real numbers a and b such that: ((5i)/(2+3i)^2)=a+bi Find the real numbers a and b such that: ((1+i)/i)-((3)/(4-i))=a+bi

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: Find the real numbers a and b such that: ((5i)/(2+3i)^2)=a+bi Find the real numbers a and b such that: ((1+i)/i)-((3)/(4-i))=a+bi      Log On


   

Question 29449: Find the real numbers a and b such that:
((5i)/(2+3i)^2)=a+bi
Find the real numbers a and b such that:
((1+i)/i)-((3)/(4-i))=a+bi
Answer by longjonsilver(2297) About Me  (Show Source):
You can put this solution on YOUR website!
I shall do the first. You do the second.

We need to convert +%28%285i%29%2F%282%2B3i%29%5E2%29+ into the form a+bi

+%285i%29%2F%282%2B3i%29%5E2+
+%285i%29%2F%28%282%2B3i%29%282%2B3i%29%29+
+%285i%29%2F%284%2B12i%2B9i%5E2%29+
+%285i%29%2F%284%2B12i-9%29+
+%285i%29%2F%2812i-5%29+
+%285i%29%2F%28-5%2B12i%29+
+%28%285i%29%2F%28-5%2B12i%29%29%2A%28%28-5-12i%29%2F%28-5-12i%29%29+ where the sexond bracket is "1"... using the conjugate of (-5+12i)

+%28%285i%29%28-5-12i%29%29%2F%28%28-5%2B12i%29%28-5-12i%29%29+
+%28-25i-60i%5E2%29%2F%2825%2B60i-60i-144i%5E2%29+
+%28-25i%2B60%29%2F%2825%2B144%29+
+%2860-25i%29%2F169+
+%2860%2F169%29-%2825%2F169%29i%29+
+%2860%2F169%29%2B%28-25%2F169%29i%29+

so a=60/169
and b = -25/169

jon.