Question

Determine the polar form of the complex

number 1 + i.

Answer 1

Answer:

Z = √2( cos45° + sin45° )

{ also refer to the attachment }

Solution:

Let the given complex number be Z.

Thus,

Z = 1 + i

or Z = 1 + 1•i

Clearly ,

Here we have ;

x = 1 (+ve)

y = 1 (+ve)

Thus,

=> r = √(x² + y²)

=> r = √(1² + 1²)

=> r = √(1 + 1)

=> r = √2

Now,

=> tanα = |y/x|

=> tanα = |1/1|

=> tanα = |1|

=> tanα = 1

=> tanα = tan45°

=> α = 45°

Also,

Since , x and y both are positive , thus the complex number Z lies in 1st quadrant.

Thus,

=> θ = α

=> θ = 45°

Hence,

The given complex number in polar form will be given as ; Z = r( Cosθ + iSinθ ) ie ;

Z = √2( cos45° + sin45° )