Write the given complex number in rectangular coordinates re

Write the given complex number in rectangular coordinates (recall that the angels are in radians) :

a.) c13 = 3cis( 4 ) = 3(cos( 4 ) + isin( 4 )

b.) c14 = 6cis()

c.) c15 = 3cis(4.2)

( a ) Consider

Z = 3cis( /4 ) = 3(cos( / 4 ) + isin( / 4 ) ) = 3e^{i(/ 4)}

here r = 3 and = / 4

Let x = rcos and y = rsin

then x = 3cos(/ 4) = 3(1/2) = 3/2 and y = 3sin(/ 4) = 3(1/2) = 3/2

Hence , the given complex number can be written in rectangular co-ordinates as z = x + iy

That is z = 3/2 + i (3/2 ) = ( 3/2 ) ( 1 + i )

b) Now consider z = 6cis( ) = 6( cos( ) + isin( ) ) = 6eⁱ

Here r = 6 and = .

Let x = rcos and y = rsin

=then x 6cos() = 6( - 1) = - 6 and y = 6sin() = 6(0) = 0

Hence , the given complex number can be written in rectangular co-ordinates as z = x + iy

That is z = - 6

( C ) Now consider z = 3cis( 4.2 ) = 3( cos(4.2 ) + isin( 4.2 ) ) = 3e^i(4.2)

Here r = 3 and = 4.2 .

Let x = rcos and y = rsin

then x = 3cos(4.2) = 3( - 0.4926082134) = - 1.470782 and y = 3sin(4.2) = 3(- 0.87157577) = -2.61473

Hence , the given complex number can be written in rectangular co-ordinates as z = x + iy

That is z = -1.470782 - i( 2.61472 )