Find the two square roots of each complex number by creating and solving polynomial equations.
z = 15 − 8i
z = 8 − 6i
z = −3 + 4i
z = −5 − 12i
z = 21 − 20i
z = 16 − 30i

1) w₁=4 - i w₂= -4 + i

2) w₁= 3 - i w₂= -3  + i

3) w₁= 1 + 2i w₂= - 1 - 2i

4) w₁= 2- 3i w₂= -2 + 3i

5) w₁= 5 - 2i w₂= -5 + 2i

6) w₁= 5 - 3i w₂= -5 + 3i

Step-by-step explanation:

The root of a complex number is given by:

where:

r: is the module of the complex number

θ: is the angle of the complex number to the positive axis x

n: index of the root

1) z = 15 − 8i  ⇒ r=17 θ= -0.4899 rad

w₁==4-i

w₂==-1+i

2) z = 8 − 6i  ⇒ r=10 θ= -0.6435 rad

w₁== 3 - i

w₂== -3  + i

3) z = −3 + 4i  ⇒ r=5 θ= -0.9316 rad

w₁== 1 + 2i

w₂== -1 - 2i

4) z = −5 − 12i  ⇒ r=13 θ= 0.4426 rad

w₁== 2- 3i

w₂== -2 + 3i

5) z = 21 − 20i  ⇒ r=29 θ= -0.8098 rad

w₁== 5 - 2i

w₂== -5 + 2i

6) z = 16 − 30i ⇒ r=34 θ= -1.0808 rad

w₁== 5 - 3i

w₂== -5 + 3i

step-by-step explanation:

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thus, the first answer choice, y = sec x, is the correct one