00:01
Hello students, these are given that to convert this complex numbers to polar form we can express them in terms of their magnitude r and argument theta.
00:13
So, for the first one 2 plus 4j magnitude r is equals to root under 2 square plus 4 square this is equals to root under 4 plus 16 equals to 2 root 5 and theta equals to arc of tan of 4 by 2 this is equals to arc tan 2 which is approximately equal to 63 .43 degree.
00:50
Similarly, for the second one minus 1 plus 5j r is equals to root 26 theta equals to arc tan of 5 by minus 1 this is approximately equal to minus 78 .69 degree.
01:16
For the third one minus 5 minus 2j r is equals to root under 29 and theta equals to arc tan of 2 by 5 this is approximately equal to 21 .80 degrees.
01:44
For the next part given that 5 into e to the power j of 30 degree comma 3 into e to the power j of minus 5 comma 8 into e to the power 4 dot 2j.
02:20
So, convert to rectangular form we can use euler's form which states that e to the power j theta is equals to cos theta plus j sin theta.
02:40
So, for the first one 5 into e to the power j 30 degree r is equals to 5 and theta is equals to 30 degree.
02:54
So, r cos theta is equals to 5 cos 30 degree which is approximately equals to 4 .33.
03:05
Similarly, r sin theta is equals to 5 into sin 30 degree which is approximately equal to 2 .5...