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In this lesson, we will learn how to use the properties of conjugate numbers to evaluate an expression.

Q1:

Find the complex conjugate of β 7 β π and the sum of this number with its complex conjugate.

Q2:

What is the conjugate of the complex number 4 + 3 π ?

Q3:

Is 8 π + 1 0 the complex conjugate of the number β 8 π + 1 0 ?

Q4:

Is it true that | π§ | = | π§ | β for all π§ ?

Q5:

Put 1 + 2 π 9 + 7 π in the form π₯ + π¦ π .

Q6:

Put β 1 2 π ( β 1 + π ) 2 in the form π₯ + π¦ π .

Q7:

Find the complex conjugate of 1 + π and the product of this number with its complex conjugate.

Q8:

Given that π₯ = ( 2 β π ) and π¦ = ( 2 + π ) , determine the value of π₯ β π₯ π¦ + π¦ 2 2 .

Q9:

Simplify 2 β 2 π 3 β π .

Q10:

Express 1 ( β 3 + π ) 2 in the form π + π π .

Q11:

Solve 2 π§ β π§ = 5 in β .

Q12:

If π = 8 + 2 π , what is π + π β ?

Q13:

Given that | π | + | π | = 1 2 , determine the value of | π π | .

Q14:

If π§ = β 8 π ,what is π§ β ?

Q15:

Is it true that π§ β π§ = 2 π ( π§ ) β I m for all π§ ?

Q16:

Is β 9 the complex conjugate of the number β 9 ?

Q17:

Is 5 the complex conjugate of the number 5?

Q18:

Given that | π | = 3 , determine the value of π π .

Q19:

Is the sum of a number and its complex conjugate always a real number?

Q20:

Is the product of a number and its complex conjugate always a real number?

Q21:

If π is the principal argument of the complex number π then what is the principal argument of π ?

Q22:

Put β 9 + π + 3 π β 5 π 5 β π + 5 π + 2 π 2 3 2 3 in the form π + π π .

Q23:

Is it true that π§ + π§ = 2 ( π§ ) β R e for all π§ ?

Q24:

If π§ is a real number, what will its conjugate be equal to?

Q25:

How do you find the conjugate of a complex number?

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