Write the complex number in the form a + bi. 3(cos 60° + i sin 60°)

Solution:

A complex number is the sum of a real number and an imaginary number.

A complex number is of the form a + ib and is usually represented by z.

Here both a and b are real numbers.

The value 'a' is called the real part which is denoted by Re(z), and 'b' is called the imaginary part Im(z).

Also, ib is called an imaginary number.

Given, 3(cos 60° + i sin 60°)

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

We know that,

Sin 60° = √3/2

Cos 60° = 1/2

Putting the values,

= 3(1/2 + i√3/2)

= 3 × (1/2) - i (3 × √3/2)

= 3/2 - i3√3/2

Therefore, the complex number in the form a + bi is 3/2 - i3√3/2.

---

Write the complex number in the form a + bi. 3(cos 60° + i sin 60°)

Summary:

The complex number  3(cos 60° + i sin 60°) in the form a+bi is 3/2 - i3√3/2.