If (x + yi) + (2(x + yi) + 3i) = 9, what is x + yi?

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.

It is given that

(x + yi) + (2(x + yi) + 3i) = 9

We can write it as

(x + yi) + 2 (x + yi) + 3i = 9

By further calculation

3 (x + yi) = 9 - 3i

Dividing both sides by 3

(x + yi) = [3(3 - i)]/3

So we get

(x + yi) = 3 - i

Therefore, x + yi is 3 - i.

If (x + yi) + (2(x + yi) + 3i) = 9, what is x + yi?

Summary:

If (x + yi) + (2(x + yi) + 3i) = 9, x + yi is 3 - i.