Simply each of the following giving your answer in the form a b e z
(2-3i)÷1+2i
To simplify (2-3i) ÷ (1+2i), we can multiply the numerator and denominator by the conjugate of the denominator, which is 1-2i.
[(2-3i)(1-2i)] ÷ [(1+2i)(1-2i)]
Simplifying the numerator:
(2-3i)(1-2i) = 2-4i-3i+6i^2 = 2-7i+6(-1) = 2-7i-6 = -4-7i
Simplifying the denominator:
(1+2i)(1-2i) = 1-2i+2i-4i^2 = 1-4i^2 = 1-4(-1) = 1+4 = 5
Now we have:
(-4-7i) ÷ 5
Dividing both real and imaginary parts by 5, we get:
-4/5 - 7i/5
So the final answer is: -4/5 - (7/5)i