Question

Find the conjugate and modulus of (bar) 9-i+ (bar) 6-i^3- (bar) 9-i^2

Answer 1

SOLUTION

TO DETERMINE

The conjugate and modulus of

$\sf{ \overline{9 - i} + \overline{6 - {i}^{3} } - \overline{9 - {i}^{2} }\: }$

CONCEPT TO BE IMPLEMENTED

In study of complex numbers for a complex number z = a + ib

1. The conjugate of z is given by

$\sf{ \overline{z} = \overline{a + ib} = a - ib }$

2. The modulus is given by

$\sf{ |z| = \sqrt{ {a}^{2} + {b}^{2} } \: }$

3. If the complex number is purely real then conjugate and modulus of the number is the number itself

EVALUATION

First we simplify the given expression

$\sf{ \overline{9 - i} + \overline{6 - {i}^{3} } - \overline{9 - {i}^{2} }\: }$

$= \sf{ \overline{9 - i} + \overline{6 - i.{i}^{2} } - \overline{9 - ( - 1) }\: }$

$= \sf{ \overline{9 - i} + \overline{6 + i} - \overline{10 }\: }$

$\sf{ = 9 + i + 6 - i - 10 \: \: }$

$= \sf{5 \: }$

Which is a purely real

Hence

The conjugate of the given number = 5

The modulus of the given number = 5

FINAL ANSWER

$\sf{ Conjugate \: of \: \: \overline{9 - i} + \overline{6 - {i}^{3} } - \overline{9 - {i}^{2} }\: } \: is \: \: 5$

$\sf{ Modulus \: of \: \: \overline{9 - i} + \overline{6 - {i}^{3} } - \overline{9 - {i}^{2} }\: } \: is \: 5$

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LEARN MORE FROM BRAINLY

Prove that

z1/z2 whole bar is equal to z1 bar/z2 bar.

Bar here means conjugate

https://brainly.in/question/16314493