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.