Express the following complex numbers in the standard form a + i b :\(

1.	Express the following complex numbers in the standard form a + i b :\(\frac{3+2i}{-2+i}\)
Answer» Given: ⇒ a + ib = \(\frac{3+2i}{-2+i}\) Multiplying and dividing with -2-i ⇒ a + ib = \(\frac{3+2i}{-2+i}\) x \(\frac{-2-i}{-2-i}\) ⇒ a + ib = \(\frac{3(-2-i)+2i(-2-i)}{(-2)^2-(i)^2}\) We know that i²=-1 ⇒ a + ib = \(\frac{-6-3i-4i-2i^2}{4-i^2}\) ⇒ a + ib = \(\frac{-6-7i-2(-1)}{4-(-1)}\) ⇒ a + ib = \(\frac{-4-7i}{5}\) ∴ The values of a, b are \(-\frac{4}{5}\), \(-\frac{7}{5}\) .

Express the following complex numbers in the standard form a + i b :\(\frac{3+2i}{-2+i}\)

Answer»

Given:

⇒ a + ib = \(\frac{3+2i}{-2+i}\)

Multiplying and dividing with -2-i

⇒ a + ib = \(\frac{3+2i}{-2+i}\) x \(\frac{-2-i}{-2-i}\)

⇒ a + ib = \(\frac{3(-2-i)+2i(-2-i)}{(-2)^2-(i)^2}\)

We know that i²=-1

⇒ a + ib = \(\frac{-6-3i-4i-2i^2}{4-i^2}\)

⇒ a + ib = \(\frac{-6-7i-2(-1)}{4-(-1)}\)

⇒ a + ib = \(\frac{-4-7i}{5}\)

∴ The values of a, b are \(-\frac{4}{5}\), \(-\frac{7}{5}\) .