Find all values of the following roots and plot them in the

Find all values of the following roots and plot them in the complex plane. square root i square root - 8i square root - 7-24i 8 square root 1 4 square root - 7 + 24i 4 square root - 1 5 square root -1 3 square root 1 + i

Solution

Post multiple questions to get the remaining answes, i have solved the first two problems

26)

(i)^(1/2) = e^(i*pi/2)

Now substituting that in the equation we get

(e^(i*pi/2))^(0.5) = e^(i*pi/4) = cos(pi/4) + isin(pi/4) = 0.7071 + 0.7071i

Similarly we will have other root as

e^(i*-3pi/4) = cos(-3pi/4) + isin(-3pi/4) = -0.7071 - 0.7071i

27)

Modulus of the function will be (8)^(1/2) = 2*sqrt(2)

Due to the negative sign, the angles on the e power will be -pi/4 and 3pi/4

2*sqrt(2) e^(-pi/4) = 2*sqrt(2) cos(-pi/4) + 2 * sqrt(2) * sin(-pi/4) * i = 2 - 2i

Similarly the other root will be -2 + 2i