Question #191f5

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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^@))#