Question #191f5

Question

1215 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-04-06T20:21:08

#-4 + 5i to sqrt41(cos(128.7^@) + isin(128.7^@))#

To convert #a + bi to r(cos(theta)+isin(theta))#

#r = sqrt(a^2 + b^2)#

#r = sqrt(-4^2+5^2)#

#r = sqrt(16+25)#

#r = sqrt(41)#

Because "a" is negative and "b" is positive we compensate for the second quadrant by adding #180^@#:

#theta = tan^-1(b/a)+180^@#

#theta = tan^-1(5/-4)+180^@#

#theta ~~ 128.7^@ #

#-4 + 5i to sqrt41(cos(128.7^@) + isin(128.87^@))#