Question

If z= 3 - 6i, then
zz
is equal to (where I=√-1)
-27
27
-45
45​

Answer 1

$\textbf{Given:}$

$\mathsf{z=3-6\,i\;where\;i=\sqrt{-1}}$

$\textbf{To find:}$

$\textsf{The value of}\;\mathsf{z\overline{z}}$

$\textbf{Solution:}$

$\mathsf{Consider,}$

$\mathsf{z=3-6\,i}$

$\mathsf{Then,\;\overline{z}=3+6\,i}$

$\mathsf{Now,}$

$\mathsf{z\overline{z}}$

$\mathsf{=(3-6\,i)(3+6\,i)}$

$\mathsf{Using,}\;\boxed{\mathsf{(a-b)(a+b)=a^2-b^2}}$

$\mathsf{=3^2-(6\,i)^2}$

$\mathsf{=3^2-6^2i^2}$

$\mathsf{=9-36(-1)}$

$\mathsf{=9+36}$

$\mathsf{=45}$

$\implies\boxed{\mathsf{z\overline{z}=45}}$

$\textbf{Find more:}}$

i^1947+i^1950 complex number​

https://brainly.in/question/20153946

If z=√37 + √-19 Find |Z|​

https://brainly.in/question/22099402

Answer 2

SOLUTION

TO CHOOSE THE CORRECT OPTION

$\sf{z = 3 - 6i \: \: then \: \: z \bar{z} = }$

• - 27

• 27

• - 45

• 45

CONCEPT TO BE IMPLEMENTED

If z is a complex number then

$\sf{z \bar{z} = { |z| }^{2} }$

EVALUATION

Here it is given that

$\sf{z = 3 - 6i \: \: }$

Now

$\sf{ |z| = \sqrt{ {3}^{2} + {6}^{2} } = \sqrt{9 + 36} = \sqrt{45} }$

Hence

$\sf{z \bar{z} }$

$\sf{ = { |z| }^{2} }$

$\sf{ = {( \sqrt{45} )}^{2} }$

$= 45$

FINAL ANSWER

Hence the correct option is 45

━━━━━━━━━━━━━━━━

Learn more from Brainly :-

1. If 4x + (3x – y)i = 3 – 6i , then values of x and y.

(a)x=3/4, y=33/4, (b) x=33/4, y=3/4 (c) x=-33/4, y=3 (d) x=-2, y=

https://brainly.in/question/29610963

2. (1-w+w2)(1-w2+w4)(1-w4+w2)...to 2n factors

https://brainly.in/question/22457549