Respuesta :

abidemiokin

Answer:

a = 1 and b = 7

Step-by-step explanation:

Given the complex expression, (3 + i)(1+2i) we are to expand it in the form a+bi as shown;

(3 + i)(1+2i)

= 3(1)+3(2i)+1(i)+i(2i)

= 3 + 6i + i + 2i²

= 3 + 71 + 2i²

According to complex notation i² = -1

;Substitute

= 3+7i+2(-1)

= 3 + 7i - 2

= 1 + 7i

Comparing 1+7i with a + bi

a = 1 and b = 7

The values of a and b are 1 and 7 respectively and this can be determined by using the arithmetic operations.

Given :

Expression -- (3 + i)(1+2i)

The following steps can be used to determine the values of 'a' and 'b':

Step 1 - Write the given expression.

= (3 + i)(1+2i)

Step 2 - Multiply 3 by (1 + 2i) and multiply i by (1 + 2i) in the above expression.

= 3 + 6i + i + 2(i[tex]\times[/tex]i)

Step 3 - The value of i[tex]\times[/tex]i = -1. So put the value (i[tex]\times[/tex]i) in the above expression.

= 3 + 6i + i - 2

Step 4 - Add 6i and i in the above expression.

= 3 + 7i -2

Step 5 - Subtract 2 from 3 in the above expression.

= 1 + 7i

Step 6 - Compare the above expression to a+bi.

a = 1

b = 7

So, the values of a and b are 1 and 7 respectively.

For more information, refer to the link given below:

https://brainly.com/question/2096984

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