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In this lesson, we will learn how to use the general formula for calculating the modulus of a complex number.

Q1:

Given that π = 8 + 4 π , find | π | .

Q2:

Given that π = 4 + π , find | π | .

Q3:

If π = 5 + 2 π and π = 5 β 2 π , what is the modulus of π + π ?

Q4:

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

Q5:

Given that π = ( π + π ) β π ( π β π ) ( π β π ) + π ( π + π ) , where π β β and π β β , write π in algebraic form and hence find | π | .

Q6:

Given that π = 3 β 9 π 1 + 3 π , determine | π | .

Q7:

Given that π = β 3 β β 3 π , find | π | .

Q8:

What is the modulus of the complex number 2 π ?

Q9:

Find the modulus and the principal amplitude of the number π = β 4 1 ( 3 0 + π 3 0 ) c o s s i n β β .

Q10:

Find the modulus and the principal amplitude of the number π = β 3 7 οΌ οΌ 5 π 3 ο β π οΌ 5 π 3 ο ο s i n c o s .

Q11:

Given that π = 3 π , find | π | .

Q12:

What is the modulus of the complex number 3 β π ?

Q13:

What is the modulus of the complex number π + π π , where π and π are real?

Q14:

Given the complex number π§ = π + π π , what is the modulus of π§ 2 ?

Q15:

What is the modulus of the complex number 3 + 7 π ?

Q16:

Find the modulus and the principal amplitude of the number π = 1 6 + 1 6 π 3 0 5 t a n β .

Q17:

Given that π = 2 β 2 β 5 π , determine | | π | | .

Q18:

If π = 1 π , where π is a complex number, what is | π | ?

Q19:

Find the modulus and principal amplitude of the complex number β 2 ( 3 0 0 + π 3 0 0 ) s i n c o s β β .

Q20:

Find the modulus and the principal amplitude of the number π = β 2 3 οΌ οΌ 3 π 2 ο β π οΌ 3 π 2 ο ο c o s s i n .

Q21:

Given that π = ( π + π ) + π ( π β π ) ( π β π ) β π ( π + π ) , where π β β and π β β , write π in algebraic form and hence find | π | .

Q22:

What is the magnitude of the product of π§ = π ( π + π π ) 1 c o s s i n and π§ = π ( π + π π ) 2 c o s s i n ?

Q23:

Given that π = 6 οΌ οΌ 3 π 4 ο + π οΌ 3 π 4 ο ο c o s s i n , find | π | .

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