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Let a and 3 be the two solutions of the quadratic equation+ v3r +1 = 0, where 0 < argo < arg 3 < 27. Consider the complex mumbers : satisfying the following three conditions: arg (1+i):+(1- i)z+k =0 < arg z

Let a and 3 be the two solutions of the quadratic equation+ v3r +1 = 0, where 0 < argo < arg 3 < 27. Consider the complex mumbers : satisfying the following three conditions: arg (1+i):+(1- i)z+k =0 < arg z

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Let a and 3 be the two solutions of the quadratic equationr+ v3r +1 = 0, where 0 < argo < urg 3 < 27. Consider the complex mumbers z satisfying the following three conditions: arg 2 (1+i)z + (1- i)3+k =0 ..... < arg 2 < R. where k is a real mumber: Let us denote the points on the complex mumber plane which express a, 3 and z by A, B and P. (1) The arguments of a and 3 are A -T and arg 8 B arg a (2) For each of in the following sentences, choose the correct answer from among ~ below. Since E from D. the point P is located on the cireumference of the circle with the center and the radius On the other hand. from 0. the point P is on the straiglit line which has the slope Jand intersects the imaginary axis at K ki. From these, we see that when n is the mmber of complex mmbers which simultane- Cusly satisty D. 2 and 3, the maximum value of n is M and in this case the range of values of k is O<k< V P where 3. 6 5 6. 6. O ZPAB 8 ZPBA 9 ZAPB
Transcribed Image Text:Let a and 3 be the two solutions of the quadratic equationr+ v3r +1 = 0, where 0 < argo < urg 3 < 27. Consider the complex mumbers z satisfying the following three conditions: arg 2 (1+i)z + (1- i)3+k =0 ..... < arg 2 < R. where k is a real mumber: Let us denote the points on the complex mumber plane which express a, 3 and z by A, B and P. (1) The arguments of a and 3 are A -T and arg 8 B arg a (2) For each of in the following sentences, choose the correct answer from among ~ below. Since E from D. the point P is located on the cireumference of the circle with the center and the radius On the other hand. from 0. the point P is on the straiglit line which has the slope Jand intersects the imaginary axis at K ki. From these, we see that when n is the mmber of complex mmbers which simultane- Cusly satisty D. 2 and 3, the maximum value of n is M and in this case the range of values of k is O<k< V P where 3. 6 5 6. 6. O ZPAB 8 ZPBA 9 ZAPB
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