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complex number(ans)

# complex number(ans) - 3 2 3 3 − − = i(d sin[cos 2 1 4 3...

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1. In each part, plot the point and sketch the vector that corresponds to the given complex number (a) 2+3i (b) -4 (c) -3-2i (d) -5i 2. Given that z=1-2i and w=4+5i. Find (a) z+w=5+3i (b) z-w=-3-7i (c) 4z=4-8i (d) 3z+4w=19+14i (e) i w z 2 13 2 13 2 3 2 1 + = + 3. Perform the calculations and express the result in the form of a+ib (a) (1+2i)(4+5i)=-6+13i (b) (2-i)(3+4i)=10+5i (c) (1+i)/(2-3i)= i 13 5 13 1 + (d) = ) 1 /( ) 3 1 ( i i i 2 3 1 2 3 1 + + (e) i i i ) 3 2 4 ( ) 3 4 2 ( ) 2 1 ( ) 3 1 ( 2 + + = +

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4. In each part, find z and |z| (a) z=2+7i i z 7 2 = , 53 | | = z (b) z=-3-5i i z 5 3 + = , 34 | | = z (c) z=5i i z 5 = , 5 | | = z (d) z=-9 9 = z , 9 | | = z (e) z=1-i i z + = 1 , 2 | | = z (f) z=1+i i z = 1 , 2 | | = z (g) 2 ) 3 1 ( i z = i z 3 2 2 + = , 4 | | = z 5. Given z=1-5i and w=3+4i, express the following in the form a+ib (a) z/w i 25 19 25 17 = (b) w z / i 25 11 25 23 + = (c) w z / i 25 19 25 17 + = 6. Express the following in the form a+ib (a) i/(1+i) i 2 1 2 1 + = (b) 2/[(1-i)(3+i)] i 2 1 2 1 + = (c) ) 3 /( ) 3 ( i i + i 2 3 2 1 + =
7. Express the following in polar form using its principle argument. (a) ] sin [cos 2 3 6 6 π i i + = + (b) )] sin( ) [cos( 2 3 6 5 6 5 i i + = + (c) i 3 3 )] sin( ) [cos(
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Unformatted text preview: 3 2 3 3 − + − = i (d) ] sin [cos 2 1 4 3 4 3 i i + = + − (e) i 3 1 − )] sin( ) [cos( 2 3 3 − + − = i (f) ) 1 )( 3 ( i i − + )] sin( ) [cos( 2 2 12 12 − + − = i (g) ) 1 /( ) 3 1 ( i i + − )] sin( ) [cos( 2 12 7 12 7 − + − = i 8. Use the De Moivre’s formula to express the following in polar form using its principle argument. (a) 100 ) 3 ( i + ] sin [cos 2 3 2 3 2 100 i + = (b) 25 19 ) 1 ( ) 3 ( i i − + − )] sin( ) [cos( 2 12 5 12 5 2 / 63 − + − = i (c) 10 211 ) 2 2 /( ] 3 3 [ i i + − (d) 2009 ) 1 ( i + − ] sin [cos 2 4 3 4 3 2 2009 i + = (e) 77 ) 3 1 ( i + (f) 10 5 ) 1 ( ) 3 ( i i − + − (g) 199 2010 ) 1 /( ) 3 1 ( i i + −...
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complex number(ans) - 3 2 3 3 − − = i(d sin[cos 2 1 4 3...

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