Question

Pls help

For z = -3 + 5i, evaluate
`$z \overline{z}.$`
(Note:
`$\overline{z}$` denotes the conjugate of z.)

Answer 1

34

Explanation:

Here z = -3 + 5i and the complement of this is

z-comp = -3 - 5i.

Multiplying these two quantities together, we get

9 -25i² = 9 + 25 = 34

Answer 2

`\underline{ \boxed{z\overline{z} = 34}}`

Explanation:

`if \: z = -3 + 5i \\then \: \overline{z} = - (3 + 5i) \\ hence \: z\overline{z} = (-3 + 5i)( - 3 - 5i) \\ z\overline{z} = 9 + 15i - 15i - {(5i)}^(2) \\ z\overline{z} = 9 - (25 ){i}^(2) \\ z\overline{z} = 9 - (25)( - 1) \\ z\overline{z} = 9 + 25 \\ \underline{ \boxed{z\overline{z} = 34}}`

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