For Q.1 to Q.10 express each complex number in form of a+ib
Question 1. (5i)(-3i/5)
Solution:
Let the given number be a,
a= (5i)*(-3i/5)
a= (-15i2)/5
a= (-3)*i2
a= (-3)*(-1)
a= 3+0i
Question 2. i9+i19
Solution:
Let the given number be a,
a = i9 * (1+i10)
a = ((i4)2*i )(1 + (i4)2 (i2))
a = (1*i)(1+i2)
a = (i)*(0)
a = 0+0i
Question 3. i-39
Solution:
Let the given number be a and let z = i39 ,
z = (i)*(i2)19
z = (i)*(-1)19
z = -i
a = i-39
a = 1/i39
a = 1/z
a = 1/-i
a = (i4)/-i
a = -i3 = -(i2*i)
a = -1*-i
a = 0+i
Question 4. 3(7+7i) + i(7+7i)
Solution:
Let the given number be a,
a = 3*(7+7i)+i*(7+7i)
a = 21+21i+7i+7i2
a = 21+7i2+28i
a = 21-7+28i
a = 14+28i
Question 5. (1-i)-(-1+i6)
Solution:
Let the given number be a,
a = (1-i)-(-1+6i)
a = 1-i+1-6i
a = 2-7i
Question 6. (1/5+2i/5)-(4+5i/2)
Solution:
Let the given number be a,
a = (1/5+2i/5)-(4+5i/2)
a = (1/5-4)+(2i/5-5i/2)
a = (-19/5)+(2/5-5/2)i
a = -19/5+(-21/10)i
a = (-38-21i)/10
Question 7. [(1/3+7i/3)+(4+i/3)]-(-4/3+i)
Solution:
Let the given number be a,
a = (1/3+7i/3)+(4+i/3)-(-4/3+i)
a = (1/3+4+4/3)+(7i/3+i/3-i)
a = (5/3+4)+(8i/3-i)
a = 17/3+ (5i/3)
a = (17+5i)/3
Question 8. (1-i)4
Solution:
Let the given number be a,
a = ((1-i)2)2
As we know , (a-b)2= (a2+b2-2ab)
a = (1+i2-2i)2
a = (1-1-2i)2
a = (-2i)2
a = 4i2
a = -4+0i
Question 9. (1/3+3i)3
Solution:
Let the given number be a,
a = (1/3+3i)3
As we know, (a+b)3= (a3+b3+3ab(a+b))
a = ((1/27)+(3i)3 +3(1/3)*(3i)(1/3+3i))
a = (1/27 +(-27i)+ 3i*(1/3+3i))
a = (1/27+(-27i)+i+9i2)
a = ((1/27)-9+(-27)i+i)
a = ((-242/27)-26i)
Question 10. (-2-(i/3))3
Solution:
Let the given number be a,
a = (-2-i/3)3
a = -((2+i/3)3)
As we know, (a+b)3= (a3+b3+3ab(a+b))
a = -((8)+(i/3)3 +3(2)*(i/3)(2+i/3))
a = -(8+(-i/27)+ 2i*(2+i/3))
a = -(8-i/27+4i+2i2/3)
a = -(8-2/3+(-i/27)+4i)
a = -(22/3 +(107i/27))
a = -22/3-107i/27