Find the quotient
z1/z2
in standard form. Convert to trigonometric form and find the quotient to check your answer.
z1=2+2i , z2=1+i
We can find the quotient by multiplying both the numerator and denominator by the complex conjugate of the denominator:
z1/z2 = (2+2i)/(1+i) = (2+2i)/(1+i) * (1-i)/(1-i) = (2+2i-2i+2)/(1+1) = 2+0i
Therefore, the quotient in standard form is 2.
To convert to trigonometric form, we can find the magnitude and argument of z1/z2:
|z1/z2| = |2| = 2
arg(z1/z2) = arg(2) = 0
Therefore, z1/z2 in trigonometric form is 2∠0.
To check our answer, we can convert z1 and z2 to polar form:
z1 = 2∠45°
z2 = √2∠45°
Then, we can find their quotient:
z1/z2 = 2∠45° / √2∠45° = (2/√2)∠0 = 2∠0
Our answer matches our earlier calculations, so we can be confident that 2 is the correct answer for the quotient in standard form and 2∠0 is the correct answer for the quotient in trigonometric form.