WRITE THE COMPLEX NUMBER IN STANDARD FORM

Example 1 :

3(cos 30˚ - i sin 30˚)

Solution :

Given, z  =  3(cos 30˚ - i sin 30˚)

By using the calculator, we get

z  =  3[√3/2 - i(1/2)]

z  =  3√3/2 - 3/2i

So, the standard form is 3√3/2 - 3/2i.

Example 2 :

8(cos 210˚ + i sin 210˚)

Solution :

Given, z  =  8(cos 210˚ + i sin 210˚)

By using the calculator, we get

z  =  8[-√3/2 + i(-1/2)]

z  =  (-8√3/2) - (8/2i)

z  =  -4√3 - 4i

So, the standard form is -4√3 - 4i.

Example 3 :

5[cos (-60˚) + i sin (-60˚)]

Solution :

Given, z  =  5[cos (-60˚) + i sin (-60˚)]

By using the calculator, we get

z  =  5[1/2 + i(-√3/2)]

z  =  (5/2) - (5√3/2)i

So, the standard form is 5/2 - (5/2)√3i.

Example 4 :

5(cos π/4 + i sin π/4)

Solution :

Given, z  =  5(cos π/4 + i sin π/4)

By using the calculator, we get

z  =  5[√2/2 + i(√2/2)]

z  =  (5/2)√2 + (5/2)√2i

So, the standard form is (5/2)√2 + (5/2)√2i.

Example 5 :

√2(cos 7π/6 + i sin 7π/6)

Solution :

Given, z  =  √2(cos 7π/6 + i sin 7π/6)

By using the calculator, we get

z  =  √2[-√3/2 + i(-1/2)]

z  =  -√6/2 - √2/2i

So, the standard form is -√6/2 - √2/2i.

Example 6 :

√7(cos π/12 + i sin π/12)

Solution :

Given, z  =  √7(cos π/12 + i sin π/12)

By using the calculator, we get

z  =  √7[((√6 + √2)/4) + i((√6 - √2)/4)]

z  =  √7[(√6 + √2)/4] + √7[(√6 - √2)/4]i

So, the standard form is 

√7[(√6 + √2)/4] + √7[(√6 - √2)/4]i

Related pages

• Find the cube root of a complex number
  
• Find the nth root of a complex number
  
• Find the indicated power of a complex number
  
• Plot the complex number in the complex plane
  

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