Answer:
a)z1 +z2 =z2 + z1 ...proved.
b) z1 + ( z2+ z3 )=(z1+z2)+z3 ... proved.
Step-by-step explanation:
It is given that there are three vectors z1 = a1 + ib1, z2 = a2 + ib2 and z3 = a3 + ib3. Now, we have to prove (a) z1 + z2 = z2 + z1 and (b) z1 + (z2 +z3) = (z1 + z2) + z3.
(a) z1 + z2 = (a1 +ib1) + (a2+ ib2) = (a1 +a2) + i(b1 +b2) {Adding the real and imaginary parts separately}
Again, z2 + z1 =(a2 +ib2) + (a1 +ib1) = (a2 +a1) + i(b2 +b1) {Adding the real and imaginary parts separately}
Hence, z1 +z2 =z2 + z1 {Since, (a1 +a2) = (a2 +a1) and (b1 +b2) = (b2 +b1)}
(b) z1 + ( z2+ z3 ) = [a1 + ib1] + [(a2 + a3 ) + i(b2 + b3 )] = ( a1 + a2 + a3) + i( b1+ b2+b3) {Adding the real and imaginary parts separately}
Again, (z1+z2)+z3 = [(a1+a2) +i(b1+b2)]+[a3+ib3] = ( a1 + a2 + a3) + i( b1+ b2+b3) {Adding the real and imaginary parts separately}
Hence, z1 + ( z2+ z3 )=(z1+z2)+z3 proved.
Answer:
C
Step-by-step explanation:
Round the decimals.
42 Feet is Greater than 180 Inches
Because: 1 Foot= 12 Inches
So: 12*42= 540 Inches.
So 42 Feet is Greater.
Answer: <em><u>5 11/12</u></em>
Step-by-step explanation:
Since they only walked on Monday, Wednesday and Thursday,
You have to add 3/4 + 1 2/3 + 3 1/2
So, 3/4 + 1 2/3 + 3 1/2 =
3/4 + 2/3 + 1/2 = 1 11/12
1 + 3 = 4
4 + 1 11/12 = 5 11/12
Kahal made an error in step 1 in his calculation.
Step-by-step explanation:
Inequality solved by Kahal;
4x-4>20
Steps used by Kahal
step 1: 4x-4>20
step 2: 4x>16
step 3: x>4
Kahal made mistake in first step where he subtracted 4 from 20. because to eliminate 4 we will add 4 on both sides which will make;
Step 1: 4x-4+4 > 20+4
4x>24
Thus,
Kahal made an error in step 1 in his calculation.
Keywords: inequality, addition
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