Question

Find the value of (5+12i), where i=−1.

• A. (A) ±(2+3i)
• B. (B) ±(3+2i)
• C. (C) ±(2−3i)
• D. (D) ±(1+2i)

Answer 1

Answer: (B)

(B) ±(3+2i)

Answer 2

Explanation:
Let, (5+12i)=x+iyOn squaring both sides we get,5+12i=(x+iy)2⇒5+12i=x2+(iy)2+2(x)(iy)⇒5+12i=x2+i2y2+2xyiAs we know,i2=−1⇒5+12i=x2+(−1)y2+2xyi⇒5+12i=(x2−y2)+(2xy)iComparing real and imaginary parts on both sides, we getx2−y2=5 and 2xy=12∴xy=6⇒y=6xNow, (x2−y2)=5Putting value of y in above equation, we getx2−(6x)2=5⇒x2−36x2=5⇒x4−36x2=5⇒x4−36=5x2⇒x4−5x2−36=0⇒x4−9x2+4x2−36=0⇒x2(x2−9)+4(x2−9)=0⇒x2−9=0 or x2+4=0⇒x2=9 or x2=−4⇒x=±3 (we know that x2 is always greater than zero so, we neglect x2=−4Now, x2−y2=5∴9−y2=5⇒y2=4⇒y=±2So, (5+12i)=±(3+2i)Hence, the correct option is (B).