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Find the product of the complex number and its conjugate.

1. 2- 3i
2. -3 + 4i
3. -1 - √2i

User EboMike
by
7.7k points

2 Answers

6 votes

The product of the complex number and its conjugate for 2- 3i, -3 + 4i, and -1 - √2i is 13, 25, and 3 + 2√2 respectively.

Let us find the product of the complex number and its conjugate for each of the complex numbers:

1. 2- 3i

The conjugate of 2- 3i is 2+3i.The product of 2- 3i and 2+3i is:

(2 - 3i)(2 + 3i)

= 4 + 6i - 6i - 9i²

= 4 + 9= 13

Therefore, the product of 2- 3i and its conjugate is 13

.2. -3 + 4i

The conjugate of -3 + 4i is -3 - 4i.The product of -3 + 4i and -3 - 4i is:

(-3 + 4i)(-3 - 4i) = 9 - 12i + 12i - 16i²

= 9 + 16

= 25

Therefore, the product of -3 + 4i and its conjugate is 25.

3. -1 - √2i

The conjugate of -1 - √2i is -1 + √2i.The product of -1 - √2i and -1 + √2i is:

(-1 - √2i)(-1 + √2i)

= 1 - √2i + √2i - (i² * 2)

= 1 + 2

= 3

Therefore, the product of -1 - √2i and its conjugate is 3.The product of -1 - √2i and its conjugate is 3 + 2√2.

Therefore, The product of the complex number and its conjugate for 2- 3i, -3 + 4i, and -1 - √2i is 13, 25, and 3 + 2√2 respectively.

User Shuwei
by
7.8k points
4 votes

Answer:

1. (2 - 3i)(2 + 3i) = 4 + 9 = 13

2. (-3 + 4i)(-3 - 4i) = 9 + 16 = 25

3. (-1 - i√2)(-1 + i√2) = 1 + 2 = 3

User Pedro Gabriel Lima
by
8.7k points
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