Write the complex number in the form a + bi. √6(cos 315° + i sin 315°)

Solution:

Given, √6(cos 315° + i sin 315°)

We have to write the complex number in the form a + bi.

We know that,

Sin 315° = -1/√2

Cos 315° = 1/√2

Putting the values,

= √6(1/√2 + i (-1/√2))

= √6(1/√2 - i1/√2)

We know, √6 = √3 × √2

= √3 × √2 (1/√2 - i1/√2)

= √3 × √2(1/√2) - i√3 × √2(1/√2)

= √3 - i√3

Therefore, the complex number in the form a+bi is √3 - i√3.

---

Write the complex number in the form a + bi. √6(cos 315° + i sin 315°)

Summary:

The complex number  √6(cos 315° + i sin 315°) in the form a+bi is √3 - i√3.