The complex number 3 + 4i is rotated about origin by an angle of π4 and then stretched 2 times. The complex number corresponding to new position is

A=3+4i B=new position of A=23+4ieiπ4=2(3+4i)1+i2=6+8i12+i2 =-2+72i =2-1+7i

The complex number 3 + 4i is rotated about origin by an angle of π4 and then stretched 2 times. The complex number corresponding to new position is

A=3+4i B=new position of A=23+4ieiπ4=2(3+4i)1+i2=6+8i12+i2 =-2+72i =2-1+7i

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The complex number 3 + 4i is rotated about origin by an angle of $\frac{π}{4}$ and then stretched 2 times. The complex number corresponding to new position is

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$\sqrt{2} (- 1 + 7 i)$

$\sqrt{2} (- 1 - 7 i)$

$\sqrt{2} (3 - 4 i)$

$\sqrt{2} (- 3 + 4 i)$

answer is B.

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Detailed Solution

$A = 3 + 4 i B = n e w p o s i t i o n o f A = 2 (3 + 4 i) e^{\frac{i π}{4}} = 2 (3 + 4 i) (\frac{1 + i}{\sqrt{2}}) = (6 + 8 i) (\frac{1}{\sqrt{2}} + \frac{i}{\sqrt{2}}) = - \sqrt{2} + 7 \sqrt{2} i = \sqrt{2} (- 1 + 7 i)$

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