Question #191f5

1 Answer
Apr 6, 2017

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

Explanation:

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^@))